JEE Class main Answered
A square loop side 20 cm is initially kept 30 cm away from a region of uniform magnetic field of 0.1 T .It is then moved towards right with a velocity of 10 mper sec till it goes out of the field plot a graph showing EMF vs t.
Asked by deepthipradeep08 | 13 May, 2021, 08:38: PM
Expert Answer
To get the plot of induced EMF as a function of time till the loop exit the uniform magnetic field region ,
we need the width of uniform magnetic field region through which the loop crosses.
But in the given question width of uniform magnetic field region is not given.
Hence this question is answered by considering the width of uniform magnetic field region is 40 cm .
It is given that initially the loop is 30 cm away from magnetic field region.
Let us assume the right edge of the loop is 30 cm away from magnetic field region.
When the right edge is moving till 30 cm from its starting position there in no induced EMF .
This initial time = distance / speed = ( 30 × 10-2 ) m / 10 m/s = 30 ms .
Hence as shown in figure, for a initial time of 30 ms , induced EMF is zero.
When the loop enters the magnetic field region , induced EMF ξ is given by Faraday's law of induction as
ξ = - dφ/dt ........................... (1)
where φ = ( B × A ) is magnetic flux , B is magnetic field induction and A is area of loop
Since magnetic field B is uniform , but flux area covered by loop is changing , we get induced EMF ξ as
ξ = - [ B × ( dA/dt ) ] = - [ B × l × ( dl/dt) ] = - ( B × l × v ).....................(2)
where l is side length of loop and v is speed of loop
When loop enters the magnetic field region, flux of magnetic field increases .
Hence according to eqn.(1) we get -ve induced EMF
Magnitude of induced EMF is calculated using eqn.(2) as follows
ξ = 0.1 ×0.2 × 10 = 0.2 v = 200 mV
We get induced EMF till the loop completely inside the magnetic field region, i.e.,
right edge of loop has travelled 20 cm inside the magnetic field region.
Time taken for the right edge to move 20 cm is 20 ms .
Hence we get induced EMF -200 mV for 20 ms as shown in figure.
Once the left edge has entered the magnetic field region , change in magnetic flux will not be there
till the right edge moves to the right boundary of magnetic field region.
Since the magnetic field region is 40 cm and loop side length is 20 cm , for another 20 cm movement
of right edge we will not get induced EMF .
This time duration is 20 ms . Hence as shown in figure, induced EMF will be zero for 20 ms
after getting initial -ve induced EMF.
Once the right edge starts exiting the right boundary, flux of magnetic field decreases
till the left edge of loop crosses the boundary of magnetic field region.
This time rate of change of magnetic flux is negative, hence we get +ve induced EMF of same
magnitude of 200 mV. Time duration of this positive induced EMF is time taken by the loop to cross
the magentic field region , i.e., 20 ms .
This positive induced EMF is shown in figure while the loop is exiting the magenetic field region.
Answered by Thiyagarajan K | 13 May, 2021, 11:09: PM
Application Videos
-
efficiency of transformer
In this video, the relation between number of turns of primary and secondar... -
Impedance of AC circuit
This video explains the impedance of an AC circuit due to resistances and r... -
LCR circuit problems - 1
This video explains the approach of solving the resistance and inductance o... -
LCR circuit problems - 2
This video describes the calculation of effective current and phase differe... -
LCR circuit problems - 3
This video focuses on the calculation of circuit impedance and potential di...
Concept Videos
-
Magnetic Flux - Part 1
This video deals with establishing a relation between electricity & magneti... -
Law of Faraday and Lenz - Part 1
This video explains Faraday's law, Lenz's law and their applications. -
Motional EMF - Part 1
This video explains the generation of motional emf due to motion of a condu... -
Eddy Currents - Part 1 ...
This video explains generation, effects and applications of eddy currents. -
AC Generator - Part 1
This video explains the alternating currents and their use, principle behin...
JEE main - Physics
Asked by kmani310507 | 28 Apr, 2024, 04:38: PM
ANSWERED BY EXPERTJEE main - Physics
Asked by dileepkumardasari665 | 08 Feb, 2024, 08:30: AM
ANSWERED BY EXPERTJEE main - Physics
Asked by nikanaujiya147 | 08 Nov, 2023, 08:23: AM
ANSWERED BY EXPERTJEE main - Physics
Asked by aaryamanmodern | 07 Aug, 2023, 10:08: PM
ANSWERED BY EXPERTJEE main - Physics
Asked by swayamagarwal2114 | 17 Jul, 2022, 12:04: PM
ANSWERED BY EXPERTJEE main - Physics
Asked by ojastej235 | 13 Nov, 2021, 12:22: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by vidyavikram10 | 18 May, 2021, 08:58: AM
ANSWERED BY EXPERTJEE main - Physics
Asked by dawarsonali783 | 15 May, 2021, 05:34: PM
ANSWERED BY EXPERTJEE main - Physics
Asked by deepthipradeep08 | 13 May, 2021, 08:38: PM
ANSWERED BY EXPERT
