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.

 

[Gene Naden]

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.