# Physics

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There are two conducting concentric hollow spheres of outer radii R2 and R1 ( R2>R1 ). The thickness of the material of both spheres is d .

The inner sphere is negatively charged with charge density -σ1, . The larger sphere is positively charged with charge density +σ2.

(a) What is the electric field (magnitude and direction) inside the inner sphere?

Direction: use units vectors in spherical coordinates ( r , Ѳ^ , ø^)

Magnitude: (Express your answer in terms of the following variables, if necessary R1, R2 , σ1 , σ2 , d , r and the constant epsilon_0 .

What is the electric field (magnitude and direction) at distance from the center of the spheres for the following values of r :

(b) r<R1 but larger than R1-d

Direction: use units vectors in spherical coordinates ( r , Ѳ^ ,ø^)

Magnitude: (Express your answer in terms of the following variables, if necessary R1 , R2 , σ1 , σ2 , d , r and the constant .

(c) r>R1 but smaller than R2-d

Direction: use units vectors in spherical coordinates ( r ,Ѳ^ , ø^ )

Magnitude: (Express your answer in terms of the following variables, if necessary , R1 , R2 ,σ1,σ2, d,r and the constant epsilon_0 .

(d) r<R2 but larger than R2-d

Direction: use units vectors in spherical coordinates ( r , Ѳ^, ø^ )

Magnitude: (Express your answer in terms of the following variables, if necessary R1 , R2 , σ1 , σ2 , d , r and the constant epsilon_0 .

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