A positively charged sphere of radius r0 carries a volume charge density ρ (figure). A spherical cavity of radius r0/2 is then scooped out and left empty. C1 is the center of the sphere and C2 that of the cavity. What is the direction and magnitude of the electric field at point B?
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a
17ρr054ε0 left
b
ρr06ε0 left
c
17ρr054ε0 right
d
ρr06ε0 right
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=ρR33ε0r2EB=Ewhole sphere −Ecavity =ρr03ε0−ρr0233ε03r022=17ρr054ε0