# A square loop of side 12 cm with its side parallel to x and y axis move with velocity of 8 cms^-1in
the positive x direction in an environment containing a magnetic field in this positive z direction.The
field is neither uniform in space nor constant in time.It has a grdient of 10^-3 Tcm^-1 along the negative x direction (i.e., it increases by 10^-3 Tcm^-1 along the negative x direction i.e.it increases
by 10^-3 Tper cm as one moves in the -ve x direction),and it is decreasing in time at the rate 10^-3
Ts^-1.Determine the direction and magnitude of the induced current in the loop if its resistance is 4.5
m ohm.

### Asked by Balbir | 26th Jul, 2017, 09:03: PM

Expert Answer:

### The following steps and pointers need to be followed for solving the query:
1) First, find the area of the loop as it is inside the field. A = 144 × 10^{-4} m^{2}.
2) Consider the time variation of the field. It is 10^{-3} Ts^{-1} With this, we get the change of flux due to time variation as (dΦ/dt)_{t} = ε_{t} = (B/t)A = 10^{-3} Ts^{-1} × 144 × 10^{-4}.
3) Flux due to motion of loop in non-uniform field is (dΦ/dt)_{v} = (B/t)Av = ε_{v}.
4) Add both the values of emf to get the total induced emf.
5) Find the induced current by I = ε/R.
6) Note that the direction of induced current will be such as to increase the current through +z direction.

^{-4}m

^{2}.

^{-3}Ts

^{-1}With this, we get the change of flux due to time variation as (dΦ/dt)

_{t}= ε

_{t}= (B/t)A = 10

^{-3}Ts

^{-1}× 144 × 10

^{-4}.

_{v}= (B/t)Av = ε

_{v}.

### Answered by Romal Bhansali | 28th Jul, 2017, 01:43: PM

## Related Videos

- 100MH coil carries a current of 5 ampere what is energy store in it
- Please solve question 2 And question 4.
- Self inductance L1
- What will be the effect on self inductance when the number of coils is doubled?
- Suppose the two coils with inductance L are connected as shown in the diagram above. Calculate the total self inductance.
- Suppose a circular coil and a conductor are kept adjacent to each other in same plane. Calculate the mutual inductance if the radius of circular coil is 'r' with 'n' number of turns kept at distance 'l' from the conductor.
- What is the difference between self inductance and mutual inductance?
- What is coefficient of coupling given L
_{1}= 4 H , L_{2}= 4 H , M = 256. - Calculate total inductance.
- Calculate the mutual inductance of a 1 m long coil with 0.4 m radius and 1000 turns has a secondary of 500 turns wound near its mid-point.

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change