# 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

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