Question

A solid insulating sphere of radius R has a non-uniform charge density that varies with the distance r from the center according to the formula p(r) = p0(exp)(-r/b)/r^2 where b and p0 are constants.

A)What type of Gaussian surface would you use in this problem?

B) Derive an expression for the electric flux trough the Gausssian surface in terms of the electric field strength E(r).

C) Derive an expression for E(r) a distance r < R from the sphere’s center in terms of the constants p0 and b. Note: The volume element for a sphere shell of radius r and thickness dr is dV = 4(pi)(r^2)dr.

Answer 1

The gaussian surface that is convenient to use would be a sphere, which can be adapted to the conditions of the charge density given in the problem.

Answer 2

Wrong pics

Answer 3

This is what I did with my classmates

Answer 4

is that correct?

Answer 5

@aliqanber

Answer 6

@aaronq , @welshfella

Answer 7

@Elsa213

Answer 8

I think your solution looks good.

Answer 9

Should b be

E(r)A = Qin/ epsalon0 ?

Answer 10

like this but inversed?

https://upload.wikimedia.org/math/6/a/8/6a81cca2936e2b38422f89853918e8de.png

Answer 11

I am just nor sure because part b says derive and I am just using the formula that the book gives.

Answer 12

I think the answer for b is just flux = integral E dA = E (4*pi*r^2)

Answer 13

and then you are 100% that the rest is fine?

Answer 14

yeah pretty sure.

Answer 15

Thanks then @aliqanber appreciate your hard work :D

Answer 16

np

Answer 17

got same