Question

Question....intuitive....(I don't have much intuition sadly)

Answer 1

hmm ... what has remained constant?

Answer 2

potential ... of course!! ... the capacitance has changed due to charges.

Answer 3

the potential

Answer 4

and use ... energy stored = work done = E.d <-- integration

Answer 5

yeah
\[U=\frac 12 CV^2\]
let's see if I can derive distance....

Answer 6

\[U=\frac 12 C V^2\]
\[d=\frac VE\]

Answer 7

\[U=\frac 12 C (dE)^2\]

Answer 8

1:9

Answer 9

1:3

Answer 10

\[U=\frac 12\frac {A\epsilon_0 V^2}{d}\]

Answer 11

this seems ok.....should I think of this in terms of proportions?

Answer 12

yep .. when you take ratio's they cancel out.