A metal bar is moving with a velocity of `v = 5 cm s^(-1)` over a U-shaped conductor. At `t = 0`, the external magnetic field is `0.1 T` direction out of the page and is increasing at a rate of `0.2 T s^(-1)`.
Tale `l = 5cm`, and at `t = 0, x = 5 cm`.

The current flowing in the circuit is

Options

A. (a) `2.5 A`
B. (b) `5 A`
C. ( c) `1 A`
D. (d) `2 A`

Answer

A

Explanation

(a) Let us take anticlockwise direction as positive, then area vector in upward direction will be positive
`phi = BA = Blx`
`e = -(dphi)/(dt) = -l[B(dx)/(dt) + x(dB)/(dt)]`
`= -5 xx 10^(-2)[0.1 xx (-5 xx 10^(-2)) + 5 xx 10^(-2) xx 0.2]`
`= -250 xx 10^(-6) V = -250 muV`
emf is coming out to be negative, so it should be clockwise.
Current: `I = (e)/(R ) = (250 xx 10^(-6))/(10^(-4)) = 2.5 A`