Question

A plane-parallel capacitor has circular plates of radius r = 10 cm, separated by a distance d =1 mm. How much charge is stored on each plate when their electric potential difference has the value V = 100 V?

Answer 1

Let's first find the capacitance of the plane-parallel capacitor:

$$C=\dfrac{\epsilon_0A}{d}=\dfrac{\epsilon_0\pi r^2}{d},$$ $$C=\dfrac{8.85\cdot10^{-12}\ \dfrac{F}{m}\cdot\pi\cdot(0.1\ m)^2}{1.0\cdot10^{-3}\ m}=2.78\cdot10^{-10}\ F.$$

Finally, we can find the charge stored on each plate of the plane-parallel capacitor when their electric potential difference has the value V = 100 V:

$$Q=CV=2.78\cdot10^{-10}\ F\cdot100\ V=27.8\cdot10^{-9}\ C=27.8\ nC.$$