What Are the Electric Field and Potential in a Non-Conducting Hollow Sphere?

[NYK]

Homework Statement

https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xaf1/v/t1.0-9/10155063_1485929725016579_7557468199677155885_n.jpg?oh=d575aa48176de7ecda27201b7ce35a5b&oe=54F7F368&__gda__=1425195231_44abd00cc231109df2fbe8d44cef9869

Homework Equations

∫E⋅da⋅n = 4πkQ_enc
ΔV(voltage) = -∫Edr

The Attempt at a Solution

To be honest I am having trouble starting the problem and defining the Q_enc for the three areas of the sphere.

I do believe that for r < R ⇒ E(r) = 2QK/r²

and for r > R ⇒ E(r) = KQ/r²

I know that the answer is listed for R<r<2R but i can't seem to come up with that answer.

I think I am just having problems with defining the Q_enc

for R<r<2R does Q_enc = 2Q_{pt charge} - Q_induced = Q sound right?

 

[vela]

Homework Statement

https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xaf1/v/t1.0-9/10155063_1485929725016579_7557468199677155885_n.jpg?oh=d575aa48176de7ecda27201b7ce35a5b&oe=54F7F368&__gda__=1425195231_44abd00cc231109df2fbe8d44cef9869

Homework Equations

∫E⋅da⋅n = 4πkQ_enc
ΔV(voltage) = -∫Edr

The Attempt at a Solution

To be honest I am having trouble starting the problem and defining the Q_enc for the three areas of the sphere.

I do believe that for r < R ⇒ E(r) = 2QK/r²

and for r > R ⇒ E(r) = KQ/r²

That's right.

I know that the answer is listed for R<r<2R but i can't seem to come up with that answer.

I think I'm just having problems with defining the Q_enc

for R<r<2R. Does Q_enc = 2Q_{pt charge} - Q_induced = Q sound right?

No. The ball is non-conducting, so there won't be any induced charges. You have a charge -Q spread out uniformly within the ball. When R < r < 2R, you have to figure out what fraction of the ball is enclosed inside of the sphere of radius r. It's a geometry problem.

 

[NYK]

That's right.No. The ball is non-conducting, so there won't be any induced charges. You have a charge -Q spread out uniformly within the ball. When R < r < 2R, you have to figure out what fraction of the ball is enclosed inside of the sphere of radius r. It's a geometry problem.

I understand that, so if it was a conducting sphere the charge would be Q_enc = Q_{pt charge} +λ(π(r²-R²))?

 

[vela]

No. How did you come up with that expression?