1. A sphere of radius R is centered at the origin. In terms of a spherical...

Transcribed Image Text:

1. A sphere of radius R is centered at the origin. In terms of a spherical coordinate system, the sphere carries a volume charge density p = kr, where k is a constant. (a) Find the electric field inside the sphere. (b) Find the potential difference between the sphere's center and any point of its surface. 2. A thin spherical shell of radius R is centered at the origin. Its surface carries a charge density To cos 0, where do is a constant. Other than this surface charge, there is no charge elsewhere. It can be shown that the scalar potential is given by the functions ∞ Vin (r, 0) = Σ A₁r¹[P₁(u)] 1=0 ∞ D₁ Vout (r, 0) = [+²+1 l=0 - [P₁(u)] for r ≤R, for r > R, where {A₁, D₁} are constants to be determined. Note that u := cos 0. Find the undetermined constants and refine the expressions of Vin and Vout. 1. A sphere of radius R is centered at the origin. In terms of a spherical coordinate system, the sphere carries a volume charge density p = kr, where k is a constant. (a) Find the electric field inside the sphere. (b) Find the potential difference between the sphere's center and any point of its surface. 2. A thin spherical shell of radius R is centered at the origin. Its surface carries a charge density To cos 0, where do is a constant. Other than this surface charge, there is no charge elsewhere. It can be shown that the scalar potential is given by the functions ∞ Vin (r, 0) = Σ A₁r¹[P₁(u)] 1=0 ∞ D₁ Vout (r, 0) = [+²+1 l=0 - [P₁(u)] for r ≤R, for r > R, where {A₁, D₁} are constants to be determined. Note that u := cos 0. Find the undetermined constants and refine the expressions of Vin and Vout.