# Change in energy of a capacitor

HunterDX77M

## Homework Statement

A 2.1 aF capacitor has a net charge of 0.5e (a positive charge, the symbol e is taken as a positive number 1.6 x 10-19 coulomb). What is the energy needed to add one electron (charge -e) to this capacitor?

## Homework Equations

Energy in a Capacitor:
$U = Q^2 \div 2C$

Where U is the energy, Q is the charge and C is the capacitance

## The Attempt at a Solution

The initial charge is +0.5e and after adding a charge of -e, the final charge would be -0.5e.
To find the energy needed:
$\Delta U = U_f - U_i \\ = \frac{(Q_f)^2 - (Q_i)^2}{2C} \\ = \frac{(-0.5e)^2 - (0.5e)^2}{2C} = 0$

Squaring the initial and final charge results in positive e/4 and subtracting these values of equal magnitude gives 0. But having 0 energy change doesn't make sense to me. What am I doing wrong here?

Thanks in advance for any help

## Answers and Replies

Staff Emeritus
A 2.1 aF capacitor has a net charge of 0.5e (a positive charge, the symbol e is taken as a positive number 1.6 x 10-19 coulomb).
So on its plates this capacitor is storing a charge difference of half an electron?

HunterDX77M
So on its plates this capacitor is storing a charge difference of half an electron?

This is indeed the problem as my Professor wrote it.

HunterDX77M
After asking him about it, my Professor responded:

"The non integer charge can come from polarization of the metal piece by an electric field, that slightly moves the position of many charges."

If that helps.

Homework Helper
Gold Member
What is the voltage on the capacitor before and after adding the charge e? What then is the difference in energy?