I have been reading electricity and magnetism by Duffin in order to understand my first year EM course. So far it has been straightforward- however, I've hit a wall when it derives the force between 2 conductors (p.117 section 5.7 if you have the book!). The book says:
Force along x = - dU/dx with Q held constant, where U=electrical energy stored(I accept this)
Elementary increment dU= 0.5QdV (i accept)
=0.5 Q^2 * d(1/c) (I accept)
=-0.5 V^2 * dC.
This I do not accept, as in the first equality, it implies V is changing (dV) yet in the last equality V is constant? I'm also unsure as to where the minus sign cam from but I assume it was a misprint.
The Attempt at a Solution
The only answer I can come up with is that the equation was meant to be
dU= 0.5 d[ V^2 * C]. But if I use this for the example of a parallel plate capacitor I get a sign error.