A point charge -2 Q is at the center of a spherical shell of radius R carrying c

Question

A point charge -2Q is at the center of a spherical shell of radius R carrying charge Q spread uniformly over its surface.

(a) What is the electric field at r = 1/2 R? (Use the following as necessary: k, Q, and R. Note that the minus sign means that the direction is radially inward.)
E =   --Direction-- outward inward

(b) What is the electric field at r = 2R?
E =   --Direction-- outward inward

(c) How would your answers change if the charge on the shell were doubled? (Select all that apply.)

The answer to (a) would not change.The answer to (b) would double.The answer to (b) would be zero.The answer to (b) would not change.The answer to (a) would be zero.The answer to (a) would double.

Explanation / Answer

part a:

consider a gaussian sphere of radius r=R/2

using gauss law:

total electric flux passing through a surface is equal to total charge enclosed.

for this gaussian sphere, charge enclosed =-2*Q

then if electric field is E,

epsilon*E*4*pi*r^2=-2*Q

==>E=-2*Q/(4*pi*epsilon*R^2/4)=-2*Q/(pi*epsilon*R^2)

as E is -ve, direction is inward.

part b:

for a gaussian sphere of radius r=2*R, charge enclosed=-2*Q+Q=-Q

then using gauss' law:

epsilon*E*4*pi*(2*R)^2=-Q

==>E=-Q/(16*epsilon*pi*R^2)

as E is -ve, direction is inward.

part c:

if charge on shell becomes 2*Q, part a will not change.

for part b, total charge enclosed=-2*Q+2*Q=0

so electric field will be zero.

hence answer to a would not change and answer to b would be zero.

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