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Ch 22 HW Problem 22.51 Problem 22.51 Negative charge -Q is distributed uniformly

ID: 585591 • Letter: C

Question

Ch 22 HW Problem 22.51 Problem 22.51 Negative charge -Q is distributed uniformly over he surface of a thin spherical insulating shell with radius R. Resources previous l 10 of 25 l next Part C Calculate the magnitude of the force that the shell exerts on a positive point charge q located a distance r R from the center of the shell (inside the shell). Express your answer in terms of the variables a, 2, r, R, and constants T and E Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining Part D This question will be shown after you complete previous question(s).

Explanation / Answer

We choose our Gaussian surface to be a sphere of radius r R:

The flux through the Gaussian surface is

  E = (EdA) = EA = (E 4 r2 )

The charge distribution is uniform. Therefore, the charge enclosed in the Gaussian sphere of radius r is

qin =  .dV =   V = ( (4/3) r3)

We can now apply Gauss’s Law and equate E = qin/0

This becomes (E 4 r2 ) =   ( (4/3) r3)/0

We can now solve for the magnitude of the electric field in the region r R

E = r/30 = Qr/40R3

So Force on charge q = F = qE = qQr/40R3