The potential of a thin spherical shell of radius R is given as V(R, 0) = 3 cos² 0 + cos 0 - 1. Both insideand outside the sphere, there is empty space with no charge density. The questions on this page are basedon this system.What is the linear combination of the two Legendre polynomials that will generate this potential (Denote aLegendre Polynomial as P₁, where I is the index of the polynomial starting from 1 = 0)?O a. 2P₁ + P₂O b. 2P3 + P₁O c. Po + P₁O d. None of the listed answers.O e. 2P₂ + P1₁Of. P3 + P2What is the radial part of the potential V(r, 0) inside the spherical shell for the Pi with the lowest l (i.e. thepre-factor of Pi)?O a. rO b. None of the listed options.O c. r/RO d. 2O e.O f.(r/R)²1/²

It is given that, The potential of a thin spherical shell of radius R is

The potential of a thin spherical shell of radius R is given as V(R,0) = 3 cos² + cos 0-1. Both inside and outside the sphere, there is empty space with no charge density. The questions on this page are based on this system. What is the linear combination of the two Legendre polynomials that will generate this potential (Denote a Legendre Polynomial as Pi, where I is the index of the polynomial starting from l = 0)? O a. 2P₁ + P2 O b. 2P3 + P₁ O c. Po + P₁ O d. None of the listed answers.

The potential of a thin spherical shell of radius R is given as V(R,0) = 3 cos² + cos 0-1. Both inside and outside the sphere, there is empty space with no charge density. The questions on this page are based on this system. What is the linear combination of the two Legendre polynomials that will generate this potential (Denote a Legendre Polynomial as Pi, where I is the index of the polynomial starting from l = 0)? O a. 2P₁ + P2 O b. 2P3 + P₁ O c. Po + P₁ O d. None of the listed answers.