# Energy stored in a Capacitor derivation

1. Jun 29, 2011

### gkangelexa

Electric potential difference is defined as the potential energy difference (work difference) per unit charge, when this charge q is moved between points b and a.
so Ub - Ua = qVba

Said in other words, if an object with charge q is moved through a potential difference Vba then its potential energy changes by an amount qVba

How do you relate those equations to this one concerning Electric energy storage in a capacitor? U = 1/2 QV

Why is W = U = 1/2QV for a capacitor
instead of W = U = qV as above?

2. Jun 29, 2011

### ZapperZ

Staff Emeritus
That's a very good question.

It is addressed here:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng2.html

The work done by the battery, let's say, in moving ALL of the charges from plate to the other is not the same for all the charges. The first one doesn't encounter much resistive force, but as more and more charges accumulate on one plate, more work has to be done to do the charge transfer. The total amount of work done at the end is the store energy and the capacitance voltage V.

So when you move a charge at the end against the potential V, you are doing work against the "full field", which is different than the stored field.

Zz.

3. Jun 29, 2011

### gkangelexa

thanks youre brilliant!