# Work needed to charge a plate

• razidan

## Homework Statement

A pair of parallel conducting plates, each measuring 30 cm X 30 cm, are separated by a gap of 1.0 mm. How much work must you do against the electric forces to charge these plates with ##+1.0 \cdot 10^{-6} C ## and ##-1.0 \cdot 10^{-6} C##, respectively?

Physics for Engineers and Scientists (Third Edition), Ohanian and Markert, Vol 2. pp 823. Q.55

## Homework Equations

##W=qV##
##V_{plates}=\frac{Qd}{\varepsilon_0 A}##

## The Attempt at a Solution

So, plugging in the numbers gives a result twice the result in the book.
This leads me to think about a field of a single plate, ##E=\frac{Q}{ 2 \varepsilon_0 A}##, but I can't figure out why. and more in general, I'm not sure what the question is describing - are the plates initially neutral. and then they are charged?

Thanks,
R.

You didn't take into account the fact that V is changing while you charge up the plate. You must integrate ##V \:dq##

razidan
You didn't take into account the fact that V is changing while you charge up the plate. You must integrate ##V \:dq##
Oh boy...
Thanks.