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JEE Main 202311 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
11 April
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2023 · 11 April · Morning Shift · Physics · Electromagnetic Induction

The magnetic field B crossing normally a square metallic plate of...

The magnetic field B crossing normally a square metallic plate of area 4m24{m}^{2} is changing with time as shown in figure. The magnitude of induced emf in the plate during t=2st = 2s to t=4st = 4s, is _____ mVmV.

The magnetic field B crossing normally a square metallic plate of area 4 m ^ 2 is changing with time as shown in

Correct answer

0

Step-by-step solution

The magnetic field B crossing normally a square metallic plate of area 4 m ^ 2 is changing with time as shown in

From the graph, it can be seen that the value of the magnetic field at t=2st = 2s is 4mT4mT, whereas the magnetic field at t=4st = 4s is 8mT8mT.

The formula to calculate the magnitude of the induced emf is given by

{εind=dϕdt=ddt(BA)=AdBdt...(1)\begin{cases}{ε}_{\text{ind}} & = & \dfrac{dϕ}{dt} \\ & = & \dfrac{d}{dt}\left(BA\right) \\ & = & A\dfrac{dB}{dt} . . . \left(1\right)\end{cases}

dBdt\dfrac{dB}{dt} is the slope of the given graph.

Hence, the value of the induced emf can be calculated as follows:

{εind=4m2×(8mT−4mT4s−2s)=8mV\begin{cases}{ε}_{\text{ind}} & = & 4{m}^{2} \times \left(\dfrac{8mT - 4mT}{4s - 2s}\right) \\ = & 8mV\end{cases}

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