Question

A rectangular loop of wire is placed in the $XY$ - plane with its side of length $3cm$ parallel to the $X$ -axis and the side of length $4cm$ parallel to the $Y$ - axis. It is moving in the positive $X$ - direction with the speed $10cm/s$. A magnetic field exists in the space with its direction parallel to the $Z$ - axis. The field decreases by $2\times 10^{-3}T/cm$ along the positive $X$ - axis and increases in time by $2\times 10^{-2}T/s$. The induced emf in the wire is

• A. $-4.8\times 10^{-5}V$
• B. $4.8\times 10^{-5}V$
• C. 0
• D. $3.6\times 10^{-5}V$

Answer 1

Answer: (C)

Induced emf in wire = Rate of change of flux
$=\frac{d}{dt}(BA)=A\left\{\left(\frac{d}{dt}B\right)+v\frac{d}{dx}B\right\}$
$=12\times 10^{-4}\left(2\times 10^{-2}+10\times 10^{-2}\times 2\times 10^{-3}\right)$
$=12\times 10^{-4}\left(2\times 10^{-2}+2\times 10^{-4}\right)$
$=24\times 10^{-4}\left(10^{-2}+10^{-4}\right)=24\times 10^{-5}V$
$=0.000024V\simeq 0V$