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

Answer 1

Answer: (B)

Let $\vec{E}$ be the electric field intensity at a point on the circumference of the ring. Then, the emf induced $\varepsilon=\oint \vec{E} \cdot d \vec{l}$
where $d \vec{l}$ is a length element of the ring. Since $|\vec{E}|$ is constant and $\vec{E} \| d \vec{l}$,
$\therefore \varepsilon=E(2 \pi r)$...(i)
Also, the induced emf is
$\varepsilon=\frac{d \phi}{d t}=\pi r^{2} \frac{d B}{d t}=\pi r^{2} x$...(ii)
Equating (i) and (ii), we get $E=\frac{r x}{2}$