# Surface Charge on Conducting Sphere

A conducting sphere of radius $$R$$ with a layer of charge $$Q$$ distributed on its surface has the electric potential everywhere in space:

$V = \begin{cases} \dfrac{1}{4\pi \epsilon_0} \dfrac{QR^2}{r^3} \sin \theta \cos \theta \cos \phi, \qquad &r>R \\ \dfrac{1}{4\pi \epsilon_0} \dfrac{Qr^2}{R^3} \sin \theta \cos \theta \cos \phi, \qquad &r<R \end{cases}.$

Which of the following gives the surface charge density on the surface of the sphere?

Note: recall that the change in electric field across either side of a conductor is equal to $$\dfrac{\sigma}{\epsilon_0}$$ where $$\sigma$$ is the surface charge density.

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