- #1

Monnn

- 2

- 0

with the separation increased from x to x+[tex]\Delta[/tex]x,

It is obvious that [tex]\Delta[/tex]U changes with 0.5[1/x - 1/(x+[tex]\Delta[/tex]x)] since C changes with 1/r. (Without the common coefficient, Q^2 over A epsilon0 or something)

And the battery which maintains the voltage difference between the plates gains energy from the system with V[tex]\Delta[/tex]Q = [1/x - 1/(x+[tex]\Delta[/tex]x)] (Note that it is without 0.5 which sticks with the energy difference)

And the work exerted on the system by moving the plates is (pressure)*(area)*(distance) an integrand over 1/r^2, which gives 0.5[1/x - 1/(x+[tex]\Delta[/tex]x)] as well (the factor 0.5 originates from that of the electrostatic pressure).

So, 0.5 is exerted on the system and it seems that it is stored in the system, as [tex]\Delta[/tex]U. Then how should I explain the work with the battery?