# I Boundary condition for dielectric sphere

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1. Nov 30, 2016

### lonewolf219

Is the potential across the boundary continuous for a dielectric sphere embedded in a dielectric material, so that the potential inside the sphere can be set equal to the potential outside of it at r=R ?

2. Nov 30, 2016

Yes. And the reason is at the boundary the most you will get is a surface charge density $\sigma_p$. The electric field from an infinite sheet of surface charge, which is what $\sigma_p$ will look like at very close range is finite, even though the field from the surface charge will point in opposite directions on opposite sides of the sheet of surface charge. Thereby, the change in potential as one traverses an infinitesimal distance across the boundary of surface charge is also infinitesimal. (The electric field sees a discontinuity as one crosses the boundary, but not the potential.)