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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 (rˆ,θˆ,ϕˆ)

b)Magnitude: (Express your answer in terms of the following variables, if necessary R1, R2, σ1, σ2, d, r and the constant ϵ0. To enter σ1 type sigma_1, for σ2 type sigma_2, for R1 type R_1, etc..)

((d) r<R2 but larger than R2−d
Direction: use units vectors in spherical coordinates (rˆ,θˆ,ϕˆ)

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