Question

Figure below shows a conducting rod of negligible resistance that can slide on a smooth U-shaped rail made of a wire of resistance $1\Omega m^{-1}$. Position of the conducting rod at $t=0$ is shown. A time dependent magnetic field $B=2T\text{(tesla)}$ is switched ON at $t=0$.

The current in the loop at $t=0$ due to induced emf is

• A. 0.16 A, clockwise
• B. 0.08 A, clockwise
• C. 0.08 A, anticlockwise
• D. Zero

Answer 1

The correct option is A 0.16 A, clockwise

Using Faraday's law of induction for induced emf, $E=-\frac{d\varphi }{dt}$
Since flux, $\varphi =B.A$
$E=-\frac{d(B.A)}{dt}=-A\frac{dB}{dt}$
Since Magnetic field, $B=2t$
$\frac{dB}{dt}=2$
Area of loop, $A=40\times 20=800c{m}^2=800\times {10}^{-4}{m}^2$
$\mid E\mid =A\frac{dB}{dt}=800\times {10}^{-4}\times 2=0.16V$
Current in the loop, $I=\frac{E}{R}=\frac{0.16}{1}=0.16A$
Magnetic field applied is perpendicularly outwards to the plane. According to Lenz's law, direction of the induced current should be such that it opposes the applied magnetic field. Hence the magnetic field induced should be perpendicularly inwards and thus direction of the current should be clockwise.