Question

The magnetic field perpendicular to the plane of a conducting ring of radius r changes at the rate $\frac{dB}{dt}$.

• A. The emf induced in the ring is $\pi r^2\frac{dB}{dt}$.
• B. The emf induced in the ring is $2\pi r\frac{dB}{dt}$.
• C. The potential difference between diametrically opposite points on the ring is half of the induced emf.
• D. All points on the ring are at the same potential.

Answer 1

Answer: (A), (D)

The correct options are
A The emf induced in the ring is $\pi r^2\frac{dB}{dt}$.
D All points on the ring are at the same potential.

$\varphi =\pi r^{2}B$

Let R $=$ resistance of the ring

$\therefore$ the current in the ring $=$ i $=$ e/R.

Consider a small element dl on the ring.

emf induced in the element $=\left(\frac{e}{2\pi r}\right)dl$.

Resistance of the element $=dR=\left(\frac{R}{2\pi r}\right)dl.$

p.d. across the element $=-idR+de$

$=-\left(\frac{e}{R}\right)\left(\frac{R}{2\pi r}\right)dl+\left(\frac{e}{2\pi r}\right)dl=0$

$\therefore$ all points on the ring are at the same potential.