JEE Main · PhysicsHard

$A parallel plate capacitor with circular plates of radius $R$ is being charged. The displacement current between the plates is equal to the conduction current in the wires. If the rate of change of the electric field between the plates is $dE/dt$, what is the magnetic field $B$ at a distance $r < R$ from the axis?$

Show correct answer & step-by-step solution

Correct answer: A — $\frac{\mu_0 \epsilon_0 r}{2} \frac{dE}{dt}$

Solution

\oint B \cdot d l = μ_{0} ϵ_{0} \frac{d}{d t} \int E \cdot d A ⟹ B (2 π r) = μ_{0} ϵ_{0} (π r^{2}) \frac{d E}{d t} ⟹ B = \frac{μ _{0} ϵ _{0} r}{2} \frac{d E}{d t}