Consider the following arrangement of two conducting hollow spheres with a point

Question

Consider the following arrangement of two conducting hollow spheres with a point charge of Q0 = 4.10 ?C at the center. The inner sphere has a radius of 0.011 m and carries a net charge of Q1= -1.50 ?C. The outer sphere has a radius of 0.041m and carries a net charge of Q2 = 5.30 ?C.
1.Calculate the magnitude of the electric field at point A located at a distance 0.021 m from the center.
2.Calculate the surface charge density on the outer surface of the outer sphere. Neglect the thickness of the sphere.

Explanation / Answer

(1) Apply Gauss' Law. From symmetry, we finda sopherical Gaussian surface is to be taken, passing thru thepoint A. Given
Q0 =4.1, r0 =0.021 Q1= -1.5 , r1 =0.021-0.011= 0.01 Q2=5.3
r2= 0.041-0.021= 0.02

The net charge enclosed is Qo +-Q1 = (4.10 -2.5) mC=1.6 mC. Applying Gauss' Law,
E =9*10 ^9 *4.1*10-6/0.021^27V/m
=8.36*10^7 nc-1 (2) The charge on the outer sphere isQ2 = 5.30 mC.         Area of the suface of the outersphere,                                A =  4?R2 = 4x3.14x(0.041)2   = 0.0211136m2           Surface chargedensity ? = Q/A =  5.30 mC/ 0.0211136 m2                                                 =251.0230372840255mC/m2   

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