Surface Charge on Conducting Sphere

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

V={14πϵ0QR2r3sinθcosθcosϕ,  r>R14πϵ0Qr2R3sinθcosθcosϕ,  r<R.V = \begin{cases} \dfrac{1}{4\pi \epsilon_0} \dfrac{QR^2}{r^3} \sin \theta \cos \theta \cos \phi, \ \ r>R \\ \dfrac{1}{4\pi \epsilon_0} \dfrac{Qr^2}{R^3} \sin \theta \cos \theta \cos \phi, \ \ 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 σϵ0,\frac{\sigma}{\epsilon_0}, where σ\sigma is the surface charge density.

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