A circular-plate capacitor with a radius of 6 cm and plate separation of 1.5 mm is being charged from a battery. At a particular instant, the charging current is 1 ìC/s. At that instant, what is the strength of the induced magnetic field 3 cm from the centre of the plates?

Question

Quizplus · Accepted Answer

The strength of the induced magnetic field at a distance $r$ from the center of a circular plate capacitor being charged can be calculated using Ampère's law in the form of the Ampère-Maxwell equation. The magnetic field $B$ at a distance $r$ from the center due to a charging current $I$ is given by $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}$ is the permeability of free space, $I = 1 \, \mu\text{C/s} = 1 \times 10^{-6} \, \text{A}$, and $r = 3 \, \text{cm} = 0.03 \, \text{m}$. Plugging these values into the formula gives $B = \frac{4\pi \times 10^{-7} \times 1 \times 10^{-6}}{2\pi \times 0.03} = 1.7 \times 10^{-12} \, \text{T}$, which matches choice C.

A Circular-Plate Capacitor with a Radius of 6 Cm and Plate