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Consider a dielectric sphere placed within a dielctric medium. There is a uniform electric field $E_0$ present throughout in the medium.

Would there be surface charge on the sphere?

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  • $\begingroup$ is the considered field is mantaines uniform throughout even after the insertion of dielectric sphere ? $\endgroup$ – Feynmans Out for Grumpy Cat May 26 '14 at 19:23
  • $\begingroup$ yes the field is constant outside the sphere $\endgroup$ – user44840 May 26 '14 at 19:23
  • $\begingroup$ that is impossible $\endgroup$ – Feynmans Out for Grumpy Cat May 26 '14 at 19:24
  • $\begingroup$ Here's the full question: A dielectric sphere of radius a and relative permittivity $\epsilon_I$ is placed within a dielectric medium of relative permittivity $\epsilon_E$, extending to infinity in which a uniform electric field $E_0$ is present. Find the resulting electrostatic potentials inside and outside the dielectric sphere. $\endgroup$ – user44840 May 26 '14 at 19:30
  • $\begingroup$ I need to know whether there would be a surface charge on the sphere or not, as that determines the boundary conditions $\endgroup$ – user44840 May 26 '14 at 19:31
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Yes, there will be a surface charge density on the sphere. Because, the field in the outer medium will polarize the molecules of the dielectric and thus, there will come some surface charge density on the sphere. Notice that the dielectric sphere would still remain electrically neutral as a whole. The electric density will appear because of the redistribution of the electric charge.

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  • $\begingroup$ But it would be weird to have a $\sigma$ in your final answer when it is not given in the question.. $\endgroup$ – user44840 May 26 '14 at 19:40

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