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Figure shows a uniformly charged hemisphere of radius R. It has a volume charge density ρ. If the electric field at a point 2R, above its center is E, then what is the electric field at the point 2Rbelow its center?

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a

ρR/6ε0+E

b

ρR/12ε0−E

c

−ρR/6εn+E

d

ρR/12ε0+E

answer is B.

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Detailed Solution

Let us complete the sphere. Electric field due to lower part at A is equal to electric field due to upper Part at B = E (given) Electric field due to lower part at B = electric fleld due to full sphere - electric field due to upper Part =kQ(2R)2−E=14πε0ρ(4/3)πR34R2−E=ρR12ε0−E

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Figure shows a uniformly charged hemisphere of radius R. It has a volume charge density ρ. If the electric field at a point 2R, above its center is E, then what is the electric field at the point 2Rbelow its center?