# Electric Potential across a Boundary

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.

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

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

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.

atyy
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.