Question

Find magnetic field on circular loop of radius $r$, placed between circular plates of capacitor of radius $R$ having displacement current $i_{d}, r < R$.

• A. $\frac{\mu_{0} i_{d} r}{2 \pi R^{2}}$
• B. $\frac{\mu_{0} i_{d}}{2 \pi R}$
• C. $\frac{\mu_{0} i_{d}}{2 \pi r}$
• D. zero

Answer 1

Answer: (A)

Consider a loop of radius $r( < R)$ between the two circular plates, placed coaxially with them. The area of the loop $=\pi r^{2}$.
By symmetry, magnetic field is equal in magnitude at all points on the loop. If $i_{d}$ is the displacement current crossing the loop and $i_{d}$ is the total displacement current between plates $i_{d}=\frac{i_{d}}{\pi R^{2}} \times \pi r^{2}$.
Using Ampere-Maxwell's law, we have
$B \cdot d l =\mu_{0} i_{d}^{\prime} $ or $ B \cdot 2 \pi r=\mu_{0} i_{d} \frac{\pi r^{2}}{\pi R^{2}} $ or $ B=\frac{\mu_{0} i_{d} r}{2 \pi R^{2}}$