Question

Two circular plates of radius $R$ are kept at distance $h$ to make a parallel plate capacitor as shown in the figure. Then the capacitance of this capacitor is:

• A. $\frac{{\epsilon }_0\pi R^2}{h}$
• B. $\frac{{\epsilon }_{0}2\pi R}{h}$
• C. $\frac{2{\epsilon }_{0}2\pi R^2}{h}$
• D. none of these

Answer 1

The correct option is A $\frac{{\epsilon }_0\pi R^2}{h}$

Capacitance of a parallel plate capacitor is: $C={\epsilon }_o\frac{A}{d}$, where ${\epsilon }_o$ is permittivity of free space, $A$ is the surface area of each plate and $d$ is the distance between the two plates.

If $R$ is the radius of the circular plate, then its area is given by $A=\pi R^2$.

Also given that $h$ is the distance between the two plates.

Hence, $C={\epsilon }_o\frac{\pi R^2}{h}=\frac{{\epsilon }_o\pi R^2}{h}$