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Q.

The diagram shows a uniformly charged hemisphere of radius R. It has volume charge density ρ. If the electric field at a point 2R distance above its centre is E, then what is the electric field at the point which is 2R below its centre?

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a

ρR/6ε0+E

b

ρR/12ε0−E

c

−ρR/6ε0+E

d

ρR/12ε0+E

answer is B.

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Detailed Solution

Let us complete the sphere. Electric field at A due to lower part = electric field at B due to upper part = E (given)Electric field at B due to lower part = electric field 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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The diagram shows a uniformly charged hemisphere of radius R. It has volume charge density ρ. If the electric field at a point 2R distance above its centre is E, then what is the electric field at the point which is 2R below its centre?