H C VERMA Solutions for Class 12-science Physics Chapter 13 - Magnetic Field due to Current

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Chapter 13 - Magnetic Field due to Current Exercise 249

Question 1

Using the formulae  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current, show that the SI units of the magnetic field B and the permeability constant  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current may be written as N/A-m and  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current respectively.

Solution 1

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Unit of B H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Now, for  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Unit of  H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 2

A current of 10A is established in a long wire along the positive Z-axis. Find the magnetic field H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current at the point (1m,0,0).

Solution 2

Magnetic field due to wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Field is along positive y-axis by the right hand thumb rule. 

Chapter 13 - Magnetic Field due to Current Exercise 250

Question 3

A copper wire of diameter 1.6mm carries a current of 20A. Find the maximum magnitude of the magnetic field H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current due to this current.

Solution 3

Maximum magnitude of magnetic field will be at the surface of wire i.e., at distance r=0.8mm from center of wire.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentmT

Question 4

A transmission wire carries a current of 100A. What would be the magnetic field B at a point on the road if the wire is 8m above the road?

Solution 4

Magnetic field due to wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentmT

Question 5

A long, straight wire carrying a current of 1.0A is placed horizontally in a uniform magnetic field H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT pointing vertically upward. Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0cm from the wire in the same horizontal plane.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 5

Magnetic field due to the wire is given by

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Net magnetic field at point P

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Net magnetic field at point Q

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 6

A long, straight wire of radius r carries a current i and placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross-section. (a) At what points will the resultant magnetic field have maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field?

Solution 6

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Magnetic field due to wire is maximum at the surface of wire.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

(b) magnetic field due to wire is maximum at the surface

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

If H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

So, If H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current then minimum magnetic field H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

If H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current then minimum magnetic field is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 7

A long, straight wire carrying a current of 30A is placed in an external, uniform magnetic field of H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT parallel to the current. Find the magnitude of the resultant magnetic field at a point 2.0cm away from the wire.

Solution 7

Magnetic field due to wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Now, field due to wire and external field are perpendicular to each other.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 8

A long, vertical wire carrying a current of 10A in the upward direction is placed in a region where a horizontal magnetic field of magnitude H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT exists from south to north. Find the point where the resultant magnetic field is zero.

Solution 8

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

Let at distance r from wire in the west direction net magnetic field is zero.

So, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentmm

Question 9

Figure shows two parallel wires separated by a distance of 4.0cm and carrying equal currents of 10A along opposite directions. Find the magnitude of the magnetic field B at points H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current andH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

 

Solution 9

Magnetic field due to long wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Both fields are perpendicular to each other

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 10

Two parallel wires carry equal currents of 10A along the same direction and are separated by a distance of 2.0cm. Find the magnetic field at a point which is 2.0cm away from each of these wires.

Solution 10

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field due to wire P and Q

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 11

Two long, straight wires, each carrying a current of 5A, are placed along the X- and Y-axes respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1m, 1m), (b) (-1m, 1m), (c) (-1m, -1m), (d) (1m, -1m).

Solution 11

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Magnetic field due to wires are of equal magnitude but in opposite direction.

So, resultant field=0.

 

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

Magnetic field due to both wires is in upward direction and is of equal magnitude.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

 

(c)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current  

Magnetic field due to wires are of equal magnitude but in opposite direction.

So, resultant field=0.

 

(d)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

Magnetic field due to both wires is in upward direction and is of equal magnitude.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 12

Four long, straight wires, each carrying a current of 5.0A, are placed in a plane as shown in figure. The points of intersection form a square of side 5.0cm. (a) Find the magnetic field at the center P of the square. (b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current are points situated on the diagonals of the square and at a distance from P that is equal to the length of the diagonal of the square. Find the magnetic fields at these points.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 12

Magnetic field due to H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current-long wire=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Let magnetic field due to wire (1), (2), (3) and (4) be H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current respectively.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

The magnetic field due all four wires at point P is equal in magnitude.

The direction of magnetic fields areH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current.

So, net magnetic field=0

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current But opposite in direction, so will cancel each other.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current But opposite in direction, so will cancel each other.

So, net magnetic field=0

At point H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 13

Figure shows a long wire bent at the middle to form a right angle. Show that the magnitudes of the magnetic field at the points P, Q, R and S are equal and find this magnitude.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Solution 13

Magnetic field at the axial point of wire is zero.

Magnetic field due to semi-infinite wire is=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field due to wire (1) and wire (2) be H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current and H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current respectively.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

At point P

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (upward)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (upward)

At point Q

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (downward)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (downward)

At point R

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (downward)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (downward)

At point S

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (upward)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (upward)

Question 14

Consider a straight piece of length x of a wire carrying a current i. Let P be a point on the perpendicular bisector of the piece, situated at a distance d from its middle point. Show that for d >>x, the magnetic field at P varies as H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current whereas for d<<x, it varies as 1/d.

Solution 14

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

Here, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field at point P

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

When d>>>x (neglecting x)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

When d<<<x (neglecting d)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 15

Consider a long piece of wire which carries a current of 10A. Find the magnitude of magnetic field due to the piece of point which makes an equilateral triangle with the ends of the piece.

Solution 15

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

Magnetic field at P

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 16

A long, straight wire carries a current i. Let H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current be the magnetic field at a point P at a distance d from the wire. Consider a section of length l of this wire such that the point P lies on a perpendicular bisector of the section. Let H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current be the magnetic field at this point due to this section only. Find the value of d/l so that H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current differs from H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current by 1%.

Solution 16

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

Magnetic field due to infinite wire H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field due to section H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Here,

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

On solving,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 17

Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. Find the magnetic field B at the center of the loop assuming uniform wires.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

 

Solution 17

Wire ABC and wire ADC are in parallel combination.

So, current will be distributed in inverse ratio of resistance.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field due to AB and BC at center of loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Net field at center=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 18

Figure shows a square loop of edge a made of a uniform wire. A current i enters the loop at the point A and leaves it at the point C. Find the magnetic field at the point P which is on the perpendicular bisector of AB at a distance a/4 from it.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

 

Solution 18

The current will be equally distributed in wire ABC and ADC as both are in parallel combination and have same resistance.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Now,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current But in opposite direction hence will cancel each other.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (upward direction)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (downward direction)

Net magnetic field

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Chapter 13 - Magnetic Field due to Current Exercise 251

Question 19

Consider the situation described in the previous problem. Suppose the current i enters the loop at the point A and leaves it at the point B. Find the magnetic field at the center of the loop.

Solution 19

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

The current in wire ADCB and wire AB will be in inverse ratio of resistance.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field at center of loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 20

The wire ABC shown in figure forms an equilateral triangle. Find the magnetic field B at the center O of the triangle assuming the wire to be uniform.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 20

The current is equally divided in both sides.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current But in opposite direction.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current But in opposite direction.

So, net magnetic field=0

Question 21

A wire of length l is bent in the form of an equilateral triangle and carries an electric current i. (a) Find the magnetic field B at the center. (b) If the wire is bent in the form of a square, what would be the value of B at the center?

Solution 21

(a)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Perpendicular distance of point O from wire PR=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Net magnetic field, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

(b)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 22

A long wire carrying a current i is bent to form a plane angleH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current. Find the magnetic field B at a point on the bisector of this angle situated at a distance x from the vertex.

Solution 22

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field at P due to single wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Net magnetic field H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 23

Find the magnetic field B at the center of a rectangular loop of length l and width b, carrying a current i.

Solution 23

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 24

A regular polygon of n sides is formed by bending a wire of total length H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current which carries a current i. (a) Find the magnetic field B at the center of the polygon. (b) By lettingH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current, deduce the expression for the magnetic field at the center of a circular current.

Solution 24

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Length of each side, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Angle by each side at center H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field by a side at center

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field by all sides

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 25

Each of the batteries shown in figure has an emf equal to 5V. Show that the magnetic field B at the point P is zero for any set values of the resistances.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 25

Net current in the circuit=0

So, magnetic field is zero at point P.

Question 26

A straight, long wire carries a current of 20A. Another wire carrying equal current is placed parallel to it. If the force acting on a length of 10cm of the second wire is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN, what is the separation between them?

Solution 26

Force per unit length between parallel wires

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentcm

Question 27

Three coplanar parallel wires, each carrying a current of 10A along the same direction, are placed with a separation 5.0cm between the consecutive ones. Find the magnitude of the magnetic force per unit length acting on the wires.

Solution 27

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

On wire (1)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN towards middle wire

On wire (2)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current But opposite in direction.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

On wire (3)

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN towards middle wire

Question 28

Two parallel wires separated by a distance of 10cm carry currents of 10A and 40A along the same direction. Where a third current should be placed so that it experiences no magnetic force?

Solution 28

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

 

Let third wire is placed in middle of both wires at a distance of x from wire carrying current of 10A

Since, no magnetic force

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

x=2cm

Question 29

Figure shows a part of an electric circuit. The wires AB, CD and EF are long and have identical resistances. The separation between the neighboring wires is 1.0cm. The wires AE and BF have negligible resistance and the ammeter reads 30A. Calculate the magnetic force per unit length of AB and CD.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 29

Current in each wire will be same as all have same resistance.

So, current= 10A in each wire.

For wire AB

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentForce due to CD wire + Force due to EF wire.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

For wire CD,

Force due to AB is equal to force due to FF wire but in opposite direction.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 30

A long, straight wire is fixed horizontally and carries a current of 50.0A. A second wire having linear mass density H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current is placed parallel to and directly above this wire at a separation of 5.0mm. What current should this second wire carry such that the magnetic repulsion can balance its weight?

Solution 30

Magnetic force between wires=weight of second wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentA

Question 31

A square loop PQRS carrying a current of 6.0A is placed near a long wire carrying 10A as shown in figure. (a) Show that the magnetic force acting on the part PQ is equal and opposite to that on the part Rs. (b) Find the magnetic force on the square loop.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 31

(a)At distance x from wire consider two small elements of length dx in wire PQ and SR.

Magnetic field is same at both location.

Force on element in PQ is in upward direction and force on element in SR is in downward direction but in opposite direction.

So, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

(b) magnetic field at SP by wireH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Force of SP wire=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN (in right direction)

magnetic field at RQ by wireH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Force of SP wire=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN (in left direction)

So, net force

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN

Question 32

A circular loop of one turn carries a current of 5.00A. If the magnetic field B at the center is 0.200mT, find the radius of the loop.

Solution 32

Magnetic field for a circular loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentcm

Question 33

A current-carrying circular coil of 100 turns and radius 5.0cm produces a magnetic field of H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT at its center. Find the value of the current.

Solution 33

Magnetic field for a circular loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentmA

Question 34

An electron makes H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current revolutions per second in a circle of radius 0.5 angstrom. Find the magnetic field B at the center of the circle.

Solution 34

Magnetic field at center

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 35

A conducting circular loop of radius a is connected to two long, straight wires. The straight wires carry current i as shown in figure. Find the magnetic field B at the center of the loop.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 35

Current in each semi-circle=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magneti field due to each semicircle is same but in opposite direction. So, net magnetic field is zero.

Chapter 13 - Magnetic Field due to Current Exercise 252

Question 36

Two circular coils of radii 5.0cm and 10cm carry equal currents of 2.0A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centers coincide. Find the magnitude of the magnetic field B at the common center of the coils if the currents in the coils are (a) in the same sense. (b) in the opposite sense.

Solution 36

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

Magnetic field due to smaller coil

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Magnetic field due to bigger coil

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

 

(a) for same direction

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

 

(b) for opposite direction

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 37

If the outer coil of the previous problem is rotated through 90H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current about a diameter, what would be the magnitude of the magnetic field B at the center?

Solution 37

Now, magnetic field due to both coils will be in perpendicular direction.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentmT

Question 38

A circular loop of radius 20cm carries a current of 10A. An electron crosses the plane of the loop with a speed of H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current m/s. The direction of motion makes an angle of 30H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current with the axis of the circle and passes through its center. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane.

Solution 38

r=20cm=0.2m

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentN

Question 39

A circular loop of radius R carries a current I. Another circular loop of radius r(<<R) carries a current i and is placed at the center of the larger loop. The planes of the two circles are at right angle to each other. Find the torque acting on the smaller loop.

Solution 39

Magnetic field due to larger loop at center=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Torque acting on smaller loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 40

A circular loop of radius r carrying a current i is held at the center of another circular loop of radius R (>>r) carrying a current I. The plane of the smaller loop makes an angle of 30H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of this force?

Solution 40

Magnetic field due to larger loop at center=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Torque acting on smaller loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Since, smaller loop is at rest

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 41

Find the magnetic field B due to a semicircular wire of radius 10.0cm carrying a current of 5.0A as its center of curvature.

Solution 41

Magnetic field due to semi-circle

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 42

A piece of wire carrying a current of 6.00A is bent in the form of a circular arc of radius 10.0cm, and it subtends an angle of 120H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current at the center. Find the magnetic field B due to this piece of wire at the center.

Solution 42

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 43

A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the center becomes zero?

Solution 43

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Let straight wire is placed at distance x from center of loop.

Since, magnetic field at center is zero.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 44

A circular coil of 200 turns has a radius of 10cm and carries a current of 2.0A. (a) Find the magnitude of the magnetic field H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current at the center of the coil. (b) At what distance from the center along the axis of the coil will the field B drop to half its value at the center? (H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current)

Solution 44

N=200 turns; R=0.1m;I=2A

(a) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentmT

 

(b) H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Here, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

x=7.66cm

Question 45

A circular loop of radius 4.0cm is placed in a horizontal plane and carries an electric current of 5.0A in the clockwise direction as seen from above. Find the magnetic field (a) at a point 3.0cm above the center of the loop. (b) At a point 3.0cm below the center of the loop.

Solution 45

(a) magnetic field along axis of a circular loop is given by

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT (downward direction)

 

(b) magnetic field along axis of a circular loop is given by

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT (downward direction)

Question 46

A charge of H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentC is distributed uniformly over a circular ring of radius 20.0cm. The ring rotates about its axis with an angular velocity of 60.0 rad/s. Find the ratio of the electric field to the magnetic field at a point on the axis at a distance of 5.00cm from the center.

Solution 46

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentC

r=20cm=0.2m

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentsec

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentA

Electric field, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentm/s

Question 47

A thin but long, hollow, cylindrical tube of radius r carries a current i along its length. Find the magnitude of the magnetic field at a distance r/2 from the surface (a) inside the tube. (b) Outside the tube.

Solution 47

(a) The current enclosed by ampere loop of radius r/2 is zero.

So, magnetic field is also zero.

 

(b) Magnetic field outside hollow cylindrical tube

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 48

A long, cylindrical tube of inner and outer radii a and b carries a current i distributed uniformly over its cross-section. Find the magnitude of the magnetic field at a point (a) just inside the tube. (b) Just outside the tube.

Solution 48

(a) The current enclosed by ampere loop inside the tube is zero. So, magnetic field is also zero.

 

(b) Consider an ampere loop just outside the tube of radius b.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 49

A long, cylindrical wire of radius b carries a current i distributed over its cross-section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.

Solution 49

Consider an ampere loop of radius 'a' with center on the axis of cylinder.

Current enclosed=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

By ampere's circuital law

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 50

A solid wire of radius 10cm carries a current of 5.0A distributed uniformly over its cross-section. Find the magnetic field B at a point at a distance (a) 2cm (b) 10cm and (c) 20cm away from the axis. Sketch a graph of B versus x for 0 < × < 20cm.

Solution 50

(a) Magnetic field inside solid wire of radius 'b' at a distance of 'a' from center of the axis of cylinder.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

 

(b) magnetic field at the surface of wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

 

(c) magnetic field at the outside of wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Question 51

Sometimes we show an idealized magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

Solution 51

Consider a point A inside the loop PQRS where B=0.

According to Ampere's circuital law,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

If there is current enclosed by the loop PQRS, then magnetic field B cannot be zero.

Whereas, we have taken magnetic field at point A to be zero.

Thus, such field is not possible.

Question 52

Two large metal sheets carry surface currents as shown in figure. The current through a strip of width dl is Kdl where K is constant. Find the magnetic field at the points P, Q and R.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

 

Solution 52

Magnetic field due to a sheet at a distance 'd' from it having current through a strip of width dl is 'Kdl' can be calculated by ampere's circuital law.

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current

 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current (independent of distance)

At point P and R

Field due to both sheets are equal in magnitude but opposite in direction. Hence, net field is zero.

At point Q

Field due to both sheets are equal and is in same direction.

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 53

Consider the situation of the previous problem. A particle having charge q and mass m is projected from the point Q in a direction going into the plane of the diagram. It is found to be describe a circle of radius r between the two plates. Find the speed of the charged particle.

Solution 53

We know that,

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 54

The magnetic field B inside a long solenoid, carrying a current of 5.00A, is H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT. Find the number of turns per unit length of the solenoid.

Solution 54

Magnetic field for solenoid

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current turns/m

Question 55

A long solenoid is fabricated by closely winding a wire of radius 0.5mm over a cylindrical nonmagnetic frame so that the successive turns nearly touch each other. What would be the magnetic field B at the center of the solenoid if it carries a current of 5A?

Solution 55

Width of each turn=1mm=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentm

No. of turns=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

Question 56

A copper wire having resistance 0.01ohm in each meter is used to wind a 400-turn solenoid of radius 1.0cm and length 20cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT near the center of the solenoid.

Solution 56

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT

No. of turns per unit length H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Resistance of the wire

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Emf

V=IR

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentvolt 

Chapter 13 - Magnetic Field due to Current Exercise 253

Question 57

A tightly-wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains ndx turns and may be approximated as a circular current i n dx. (a) Write the magnetic field at the center of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the center of the solenoid. (b) Verify that if l>>a, the field tends to H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current and if a>>l, the field tends toH-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current. Interpret these results.

Solution 57

(a) Magnetic field at the axis due to the circular loop

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Here, radius=a distance of the center of the solenoid from the center of circular current=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

For the whole solenoid

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

(b) when l>>>a

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

So, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

If a>>>l

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

So, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 58

A tightly-wound, long solenoid carries a current of 2.00A. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentrev/s. Find the number of turns per meter in the solenoid.

Solution 58

Frequency of particle in uniform magnetic field

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 59

A tightly-wound, long solenoid has n turns per unit length, a radius r and carries a current i. A particle having charge q and mass m is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid?

Solution 59

The particle will undergo uniform circular motion. For particle not to strike with solenoid, radius is r/2.

Radius=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 60

A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the center of the solenoid is found to be zero. (a) Find the current in the solenoid. (b) If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its center?

Solution 60

Magnetic field due to the metal sheet H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Magnetic field due to solenoid H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

(a) Magnetic field is zero.

So, H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

 

(b) Now, field due to sheet and solenoid is perpendicular

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

Question 61

A capacitor of capacitance 100H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current is connected to a battery of 20volts for a long time and then disconnected from it. It is now connected across a long solenoid having 4000 turns per meter. It is found that the potential difference across the capacitor drops to 90% of its maximum value in 2.0seconds. Estimate the average the magnetic field produced at the center of the solenoid during this period.

Solution 61

C=100H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current; V=20volt

Q=CV

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentC

Now, potential drops to 90%

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Currentvolt

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentC

Average current flown=H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentA

Magnetic field at center of solenoid

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To Current 

H-c-verma Solutions Cbse Class 12-science Physics Chapter - Magnetic Field Due To CurrentT