Question

Potential in spherical capacitor using laplace's equation

The inner and outer radii of a sphere are Ri and Ro, respectively. A material with the permittivity value of ε fills the medium between the shells of the sphere. The shell inside has the potential value of V1 and the shell outside has the potential value of V2. By solving the proper equation, find the potential for Ro ≤ R

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Answer #1

(1 Ro Here we will use Laplace etuation in spherical Coordinates. By Raplace equation in spherical Coordinates av + rsino aoV2 at Ro 2 so) so, v= -(v1-V2) RoRi ay V, at Ri Vi=- A to ... Ri V2 = I +B Ro Solving equation ① and ② A = (V-V2) RoRi B = VI

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