Question

Concentric Spheres problem. An insulating solid charged sphere is centered in a conducting shell. The Conducting shell is not charged. I need to find the electric potential on the surface of the insulating sphere. Any ideas? I have some questions that someone might be able to answer.

Answer 1

My textbook hardly explains this section.

Answer 2

can u put up 1 ques pls?
i can try

Answer 3

Okay, so i believe to calculate the electric potential at the surface of the insulator I would use the integral \[-\int\limits_{infinity}^{a}k( Q _{enclosed}/x^{2})dx\]. But I am not sure what to use for Q enclosed. I am not sure if this is even right.

Answer 4

do u need it right now?

Answer 5

I suppose I have some time. Till 8am tomorrow and it is 2:43pm here.

Answer 6

will reply u after 6 hours..
its 1.15 am here :P

Answer 7

But clearly my method is wrong because I didn't include the conducting shell but I don't see how to include it.

Answer 8

That integral is correct, more or less. The total charge Q is just a constant, so you don't have to worry about it. The only trick is recognizing that you must integrate from infinity to the outer edge of the shell, and then from the inner edge of the shell to the surface of the solid sphere. You don't gain any potential from moving INSIDE the sphere, where the electric field is zero.

Answer 9

i think u ll get a reply !!!!!!
gud luck...dont wana use brains anymore. gn :)

Answer 10

shoot, not inside the sphere, inside the shell *** :)

Answer 11

bare with me. if i don't respond immediately its cause i am thinking.

Answer 12

yeah the potential is constant inside the shell. I got that to be -21649.5V by kQ/c

Answer 13

\[ \Phi = -k Q \left(\int_{-\infty}^c \frac{1}{x^2}dx + \int_b^a \frac{1}{x^2}dx \right) = kQ\left(\frac{1}{c} +\frac{1}{a} - \frac{1}{b} \right)\]

Answer 14

flux? is that supposed to be voltage?

Answer 15

If there was no conducting shell would it just be the second integral?

Answer 16

replacing b with infinity

Answer 17

It's voltage... it doesn't matter what symbol you use, I use that one. And if there was no shell, b and c would be the same.

Answer 18

Thanks for your help Jemurray3. I almost completely understand. I will continue working through the problems and see if I come across any other confusions.