- #1
Loro
- 80
- 1
Hi, I thought that I understood why, once the free charges stop moving, ##E=0## inside a conductor, but I really don't. Can someone please help me out?
I've heard the following arguments, but I don't think I understand any of them:
I've heard the following arguments, but I don't think I understand any of them:
- I don't think ##q=0## implies ##\vec{E}=0##. I understand that charges end up on the surface, because they experience forces, following from each other's electric fields. Therefore they distribute themselves on the surface of the conductor, such that the electric field lines are perpendicular to the surface of the conductor. Thus, I agree that ##q=0## inside the conductor, but it doesn't imply that ##\vec{E}=0## inside. ##\vec{E}## could be non-zero, but if there are no charges inside, there's nothing to experience a force, so there is equilibrium nevertheless.
- I don't think the Gauss's law proves anything either. In the integral form ##q=0## implies that ##\oint\vec{E}\cdot \text{d}\vec{A}=0##. But it doesn't mean that ##\vec{E}=0##. ##\vec{E}## could be non-uniform, so in general there's no problem with having a vanishing flux, but non-vanishing ##\vec{E}##. In the differential form ##q=0## implies ##\vec{\nabla}\cdot\vec{E}=0##, but we could have a non-zero field with vanishing divergence, there's no problem with that.
- If that matters, I don't think ##\vec{E}=0## implies ##q=0## either. Even if ##\vec{E}=0## inside a conductor, this itself doesn't imply to me that the free charge has to be vanishing inside. People say that charges won't stop moving until ##\vec{E}=0##. But suppose we have a conducting perfect solid sphere with the free charge already distributed on the surface. It can be shown from the Coulomb's law, that ##\vec{E}=0## inside. But that means that if I put a point charge of the same sign as the surface charges, in the very center of the sphere, it won't feel any force. Also, the free charges on the surface would still remain in equilibrium. But now ##\vec{E}\neq 0## inside the sphere, while we still have equilibrium.