- #1
eoghan
- 207
- 7
Hi! Suppose I have a wire with a potential difference V=bx where b is a constant. Then there is an electric field which is constant: E=b through out the wire. Well, now consider this relation:
[tex]I=\frac{dq}{dt}=\frac{d}{dt}\epsilon_0\int{\vec{E}\cdot\hat{n}dS}=\epsilon_0 S \frac{dE}{dt}=0[/tex]
where I used the Gauss' theorem and the fact that E is constant.
From this relation then follows that the electric current is 0! But I do have an electric current in the wire! Where am I wrong?
[tex]I=\frac{dq}{dt}=\frac{d}{dt}\epsilon_0\int{\vec{E}\cdot\hat{n}dS}=\epsilon_0 S \frac{dE}{dt}=0[/tex]
where I used the Gauss' theorem and the fact that E is constant.
From this relation then follows that the electric current is 0! But I do have an electric current in the wire! Where am I wrong?