# Homework Help: Electric Potential in an Insulating Sphere

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1. Sep 19, 2015

### h2obc33

1. The problem statement, all variables and given/known data
A solid insulating sphere of radius a = 4.3 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -421 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 14.6 cm, and outer radius c = 16.6 cm.

1) What is Ex(P), the x-component of the electric field at point P, located a distance d = 31 cm from the origin along the x-axis as shown? I got the answer correct: -13130.92 N/C

2) What is V(b), the electric potential at the inner surface of the conducting shell? Define the potential to be zero at infinity.

I am having trouble with number 2. I only have one more chance to submit an answer for number 2 so I can really use some help.
2. Relevant equations
ΔV=-∫E*dr
E = kQ/r
3. The attempt at a solution
For number 2 I took the integral infinity to c ∫E*dr and from c to b (which I assumed to be 0 since it is the shell) and then to calculate the integral I got (k(Q(calculated in q1)+q(of inner sphere determined by density)/c). I got -7.119E14. What did I do wrong?
For my first try I did (kq(innersphere))/b and got the message " It looks like you have calculated the potential at the inner radius of the shell to be equal to the potential at r = c produced by the insulating sphere by itself. The conducting shell plays a role here. Go back to the definition of the potential to determine the answer." But I'm not quite sure what that means.
I have also just considered that it might be the answer to number 1 (if that would be the E for the region) divided by c. Does that make sense? I'm kinda confused and afraid to guess.

2. Sep 19, 2015

### Orodruin

Staff Emeritus
What is the total charge inside a spherical surface of radius R > c?