Question

A square non-conducting loop, $20\, cm$, on a side is placed in a magnetic field. The centre of side $A B$ coincides with the centre of magnetic field. The magnetic field is increasing at the rate of $2\, T / s$. 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 $B C$ and centre $O$ is $10 \, cm$. Component of induced electric field along the rod $=\frac{d}{2} \frac{d B}{d t}$,
where $d=$ perpendicular distance from centre to the rod.
Hence, potential difference between the ends of rod.
$V =E l=l \cdot \frac{d}{2} \frac{d B}{d t}$
$=\frac{10}{2} \times 10^{-2} \times 20 \times 10^{-2} 2$
$=20\, mV$