Question

A spherical dielectric shell has inner radius r_{1},
outer radius r_{2}, and dielectric constant k. A charge Q
is placed at the center of the sphere.

(a) Determine the polarization P in the dielectric shell.

(b) Find the bound volume charge density, ρ_{b}, inside
the dielectric shell.

(c) Find the bound surface charge density, σ_{b}, at r =
r_{1} and r = r_{2}.

Answer #1

Answer question

Given a spherical dielectric shell (inner radius a, outer radius
b, dielectric constant k) and a point charge q, infinitely
separated. Now let the point charge be placed at the center of the
dielectric shell. Determine the change in energy of the system?

Charge is distributed throughout a spherical shell of inner
radius r1 and outer radius r2 with a volume density given by ρ = ρ0
r1/r, where ρ0 is a constant. Determine the electric field due to
this charge as a function of r, the distance from the center of the
shell.
In this problem the volume charge density ρ is not uniform; it
is a function of r (distance from the center.)

Answer with a drawing please!
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b) R1<r<R2
c) r>R2

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