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

`\sigma=3.72* 10^(-6)\ C/m^2`

Step-by-step explanation:

Given that,

Charge,
`q=1.4\ \mu C=1.4* 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=(\sigma)/(\epsilon_o)`

`E=(F)/(q)`

`(F)/(q)=(\sigma)/(\epsilon_o)`

`\sigma=(F.\epsilon_o)/(q)`

`\sigma=(0.59* 8.85* 10^(-12))/(1.4* 10^(-6))`

`\sigma=3.72* 10^(-6)\ C/m^2`

So, the charge density on either plate of the capacitor is
`3.72* 10^(-6)\ C/m^2`. Hence, this the required solution.