A metal sphere of radius a is surrounded by a metal shell of inner radius b and

Question

A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 0.55Q/Epsilon and the flux through a spherical Gaussian surface just outside R is 1.45Q/Epsilon0. What is the total charge on the inner sphere? (Express your answer as a multiple of Q. For example, if the total charge is 0.2Q, then input 0.2). Submit Answer Tries 0/15 What is the surface charge density of the inner sphere? (Express your answer as a multiple of Q/a2.) Submit Answer Tries 0/15 What is the total charge on the inner surface of the outer sphere? (Express your answer as a multiple of Q.) Submit Answer Tries 0/15 What is the surface charge density of the outer surface of the outer sphere? (Express your answer as a multiple of Q/R2.) Submit Answer Tries 0/15

Explanation / Answer

gauss law: it states that total flux passing through a closed surface is charge enclosed by the surface divided by electrical permitivity..

part 1:

for a gaussian surface between a and b, charge enclosed =charge on inner sphere.

hence charge on inner sphere=epsilon*flux =0.55*Q

answer to be input is 0.55
part 2:

surface charge density=charge/surface area=0.55*Q/(4*pi*a^2)

=0.04376*Q/a^2

answer to be input is 0.04376

part 3:

on inner surface of outer sphere, charge will be negative of charge on the inner sphere.

hence answer will be -0.55

part 4.

on outer surface charge=epsilon*flux =1.45*Q

then charge density=charge/surface area
=1.45*Q/(4*pi*R^2)=0.115387*Q/R^2

answer to be input as 0.115387

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