Problem 1. Here is a neutral conducting sphere with a cavity. At the center of t

Question

Problem 1. Here is a neutral conducting sphere with a cavity. At the center of the cavity lies a point charge, +9Q (positive 9Q).

(a) Use Guass's law to determine the direction and magnitude of the electric field as a function of the distance from the sphere's center. Show all your work, including a Gaussian surface.

E(r) = for 0 < r < a

E(r)= for a < r < b

E(r)= for b < r

Problem 1. Here is a neutral conducting sphere with a cavity. charge, +9 Q (positive 9 Q) At the center of the cavity lies a point (a) Use Gauss's law to determine the direction and magnitude of the electric field as a function of the distance from the sphere's center. Show all your work, including a Gaussian surface. for 0

Explanation / Answer

Here, for the conducting shell

charge on the inner shell = - charge inside the shell

charge on the inner shell = - 9Q

Now, for the charge on the outer shell

charge on outer shell + charge on inner shell = 0

charge on outer shell -9Q = 0

charge on outer shell = 9Q

Now, for the electric field

for 0 < r < a

E = k* 9Q/r^2

a < r < b

E = k*(9Q - 9Q)/r^2

E = 0

the electric field is Zero

b < r

E = k*(9Q + 9Q -9Q)/r^2

E = k * 9Q/r^2

the electric field is k* 9Q/r^2

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