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