Electric Potential across a Boundary

1. Aug 21, 2008

Apteronotus

Hi everyone,

I have a uniform electric field in which I place an object. I have read that the electric potential inside my object, $$\Phi_{in}$$, and the one on the outside, $$\Phi_{out}$$ must be equal at the boundary.
(ie. $$\Phi_{in}$$=$$\Phi_{out}$$ on the boundary)
I dont understand why this is so. Can anyone shed some light.

2. Aug 21, 2008

weejee

Otherwise the electric field(=gradiant of the potential) at the boundary will diverge.

3. Aug 21, 2008

Apteronotus

I really have no background in physics or electricity. Could you explain further?
1. what do you mean diverge?
2. why would it diverge?

4. Aug 21, 2008

weejee

1. I mean that the magnitude of the electric field is infinite.
2. $-\frac{\partial \Phi}{\partial x_i}=E_i$.
This implies that if the potential changes abruptly the electric field will be infinitely strong.

5. Aug 22, 2008

atyy

Hmmm, is that true? Seems it should depend on whether there is charge on the boundary, whether the boundary is made of metal or of plastic etc. And also whether the electrons are moving, or have reached their final positions.

6. Aug 26, 2008

Apteronotus

I'm assuming an electrostatic case, so I guess the electrons would not be moving. Second, there are no free charges on the boundary.
I'm not really sure how the boundary material would come into play.

7. Aug 26, 2008

granpa

the electric field would be infinite if the potential jumped at the boundary. divergence would be acceptable. one will get surface charges even with an insulator (dielectric).