Question

A square frame of side $10cm$ and a long straight wire carrying current $1A$ are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10m{s}^{-1}$ (see figure). The e.m.f induced in the frame at the time the left arm is at $x=10cm$ from the wire is :

• A. $2\mu V$
• B. $1\mu V$
• C. $0.75\mu V$
• D. $0.5\mu V$

Answer 1

The correct option is B $1\mu V$

In given fig $x=15$ because left arm of the frame is at $10cm$ from the wire. and $a=10cm$.

emf in $AD⟹e_1⟹\frac{a{\mu }_{o}iv}{2\pi (x-a/2)}$

emf in $EF⟹e_2⟹\frac{a{\mu }_{o}iv}{2\pi (x+a/2)}$

Net emf$=e_1-e_2$$=\frac{a{\mu }_{o}iv}{2\pi (x-a/2)}$$-\frac{a{\mu }_{o}iv}{2\pi (x+a/2)}$

putting the given values into the equation we get,

emf induced$=1.3\mu V\approx 1\mu V$