Question

A conducting ring of radius r is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is x, the electric field intensity at any point of the ring is

• A. rx
• B. $\frac{rx}{2}$
• C. 2rx
• D. $\frac{4r}{x}$

Answer 1

Answer: (B)

$\frac{rx}{2}$

Answer 2

Let $\overset{\rightarrow}{E}$ be the electric field intensity at a pint on the circumference of the ring then the emf induced $\varepsilon = \oint_{}^{}{\overset{\rightarrow}{E}.d\overset{\rightarrow}{l}}$ where $\overset{\rightarrow}{dl}$ is a length element of the ring since $\overset{\rightarrow}{E}||d\overset{\rightarrow}{l}$

$\varepsilon = E(2\pi r)$ …… (i)

Also the induced emf is

$\varepsilon = \frac{d\varphi}{dt} = \pi r^{2}\frac{dB}{dt} = \pi r^{2}x$ ……. (ii)

Equating (i) and (ii) we get

$E = \frac{rx}{2}$