Question

A square non-conducting loop, $20cm$, on a side is placed in a magnetic field. The centre of side $AB$ coincides with the centre of magnetic field. The magnetic field is increasing at the rate of $2T/s$. The potential difference between $B$ and C is

• A. 30 mV
• B. zero
• C. 10 mV
• D. 20 mV

Answer 1

Answer: (D)

Perpendicular distance between $BC$ and centre $O$ is $10cm$. Component of induced electric field along the rod $=\frac{d}{2}\frac{dB}{dt}$,
where $d=$ perpendicular distance from centre to the rod.
Hence, potential difference between the ends of rod.
$V=El=l\cdot \frac{d}{2}\frac{dB}{dt}$
$=\frac{10}{2}\times 10^{-2}\times 20\times 10^{-2}2$
$=20mV$