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.
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Transcribed Image Text:The potential of a thin spherical shell of radius R is given as V(R, 0) = 3 cos² 0 + 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 P₁, where I is the index of the polynomial starting from 1 = 0)?
O a. 2P₁ + P₂
O b. 2P3 + P₁
O c. Po + P₁
O d. None of the listed answers.
O e. 2P₂ + P1₁
Of. P3 + P2
What is the radial part of the potential V(r, 0) inside the spherical shell for the Pi with the lowest l (i.e. the
pre-factor of Pi)?
O a. r
O b. None of the listed options.
O c. r/R
O d. 2
O e.
O f.
(r/R)²
1/²
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