First slide

Maxwell's Equations

Question

A circular ring of radius r is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B = Kt, where K is a constant and r is the time. The electric field in the ring is

Moderate

A

$\frac{Kr}{4}$
B

$\frac{Kr}{3}$
C

$\frac{Kr}{2}$
D

$\frac{K}{2 r}$

Solution

$∮ \vec{E} d \vec{l} = \frac{{dϕ}_{B}}{dt}$
$or E 2 πr = \frac{d}{dt} (Kt \times {πr}^{2})$
$or E = \frac{Kr}{2}$

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