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 Q_0 = 3.50 mu C at the center. The inner sphere has a radius of 0.011 m and carries a net charge of Q_1 = -2.70 mu C. The outer sphere has a radius of 0.061m and carries a net charge of Q_2 = 5.50 mu C. Calculate the magnitude of located at a distance 0.021 A i electric field at point A from the center. Calculate the surface charge density on the outer surface of the outer sphere. Neglect the thickness of the sphere.

Explanation / Answer

as per gauss law, total electric flux passing through a gaussian surface

is equal to charge enclosed by it.

consider a gaussian sphere of radius 0.021 m

then charge enclosed by this sphere=Q0+Q1=3.5 uC -2.7 uC=0.8 uC

if electric field is E,

then epsilon*E*4*pi*0.021^2=charge enclosed=0.8*10^(-6)

==>E=0.8*10^(-6)/(4*pi*0.021^2*8.85*10^(-12))=16.3116*10^(6) N/C

part B:

charge appearing in the inner surface of outer sphere=-(Q0+Q1)=-0.8 uC

then if charge on outer surface of outer sphere is Q,

then Q-0.8 uC=Q2

==>Q=5.5 uC+0.8 uC=6.3 uC

hence charge appearing on outer surface of outer sphere is 6.3 uC

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