A solid conducting sphere of radius R is embedded in an electrically neutral non

Question

A solid conducting sphere of radius R is embedded in an electrically neutral nonconducting spherical shell that has inner radius R, has outer radius 2R, and is made of a material having dielectric constant. Inside the shell the electric field magnitude isE=3Q/(40r2) and, relative to a potential of zero at infinity, the potential at the surface of the sphere is +15Q/(160R), where Q is a constant with dimensions of electrical charge.

a) What is the charge on the sphere?

Express your answer in terms of some or all of the variables R, Q, the permittivity constant 0, and .

b) What is the dielectric constant of the shell?

Express your answer using two significant digits.

Explanation / Answer

Here ,

sphere radius , R

outer radius = 2R

a)

E = 3Q/(4*pi * epsilion_0*r^2)

as the electric field inside the shell is 3Q/(4*pi * epsilion_0*r^2)

the charge on the sphere is 3Q

b)

let the dielectric contant is k

as the potential at the surface of the shell is k

as V = 1/(4pi * epsilon_0 * k) * Q/(R)

15Q/(160R) = 1/(4pi * epsilon_0 * k) * 3Q/(R)

solving for k

k = 5/4 = 1.25

the dielectric constant is 1.25

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