SEPARATION OF VARIABLES - SPHERICAL The potential on the surface of a sphere (radius R) is given by V=V0 cos(2). (Assume V(r=[infinity])=0. Also assume there is no charge in or outside, it's ALL on the surface!) a) Find the potential everywhere inside and outside this sphere. (Hint: Can you express cos(2) as a simple linear combination of Legendre polynomials? ) b) Find the charge density () on the surface of the sphere in part a. Sketch or draw it!

a) Vin(r,θ)=(-Vo/3)+(4Vo/3R^2)r^2P2cosθ

b)σ(θ)=((Voεo)/3R)(20P2cosθ-1)

Explanation:

Due to the complex variables used to solve this exercise, the solution and the explanation are in the image

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

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