A particle of charge -60nC is placed at the center of anon-conducting spherical

Question

A particle of charge -60nC is placed at the center of anon-conducting spherical shell of inner radius 20cm and outerradius 25cm. The spherical shell is uniformly charged with acharge density of -1.33C/m3. A proton movesin a circular orbit just outside the spherical shell. Calculate the speed of the proton.

I know that I need to find the electric fields and from there findthe forces acting on the proton in order to figure out thecentripetal acceleration, but I am not sure how to set up theintegrals for the electric fields and forces.

Explanation / Answer

q = -60 nC, r = 20 cm, R = 25 cm, = -1.33C/m3 volume of the shell V = 4(R3 -r3)/3 charge of the shell Q = V = -42.48 nC use Gauss law, E = (q + Q)/(40R2) =1.4757*104 N/C qE = mv2/R v = (qER/m) = 5.94*105 m/s

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