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## 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:

[itex]U = Q^2 \div 2C[/itex]

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:

[itex]\Delta U = U_f - U_i \\

= \frac{(Q_f)^2 - (Q_i)^2}{2C} \\

= \frac{(-0.5e)^2 - (0.5e)^2}{2C}

= 0[/itex]

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