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Q.

A positively charged sphere of radius ro carries a volume charge density ρE. A spherical cavity of radius r0/2 is then scooped out and left empty, as shown. What is the direction and magnitude of the electric field at point B?

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a

17ρr054ε0left

b

ρr06ε0 left

c

17ρr054ε0right

d

ρr06ε0right

answer is A.

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Detailed Solution

Electric field on surface of a uniformly charged sphere is given byQ4πε0R2=ρR3ε0Electric field at outside point is given byE=Q4πε0r2=ρR33ε0r2E¯rat B=Esphere-Ecavity=ρr03ε0-ρr0233ε03r022=17ρr054ε0
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