Question

A 1.4-µC point charge is placed between the plates of a parallel plate capacitor. The charge experiences a force of 0.59 N. What is the magnitude σ of the charge density on either plate of the capacitor?

Answer 1

Answer:

$\sigma=3.72\times 10^{-6}\ C/m^2$

Explanation:

Given that,

Charge, $q=1.4\ \mu C=1.4\times 10^{-6}\ C$

Force experienced by the charge, F = 0.59 N

We need to find the magnitude of charge density on either plate of the capacitor. Electric field on parallel plate capacitor is given by :

$E=\dfrac{\sigma}{\epsilon_o}$

$E=\dfrac{F}{q}$

$\dfrac{F}{q}=\dfrac{\sigma}{\epsilon_o}$

$\sigma=\dfrac{F.\epsilon_o}{q}$

$\sigma=\dfrac{0.59\times 8.85\times 10^{-12}}{1.4\times 10^{-6}}$

$\sigma=3.72\times 10^{-6}\ C/m^2$

So, the charge density on either plate of the capacitor is $3.72\times 10^{-6}\ C/m^2$. Hence, this the required solution.