Question

Who can explain to me whats the difference between the U=qV and U=1/2*Q*V=1/2*C*V^2 ?

Answer 1

They are the same

Answer 2

W=U=1/2 QV=1/2 CV^2=1/2 Q^2/C

Answer 3

but how about u = qv?

Answer 4

You should write:\[U=Q.V _{ext}\;\; and\;\; U=\frac{1}{2}Q\:V\]In the first equation, test-charge Q is located in an external potential Vext (created by other charges not mentioned in the expression.

In the second equation, the charge Q is 'self-creating' the potential V in which it is, hence the factor 1/2, meaning a charge Q self-creating a potential V has half as much energy as the same charge Q put in an external potential of value V.