Question

# Three negative point charges - q each, and three positive point charges + q. + q and + Q are placed at the vertices of a regular hexagon as shown in Fig. 20.16. For what value of Q will the electric field at centre O due to the five charges at A, B, D, E and F be twice the electric field at centre O due to charge Q at C alone?

A

q

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B

q2

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C

2q

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D

5q

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Solution

## The correct option is B q2 The electric fields at centre O due to charges -q at A and D are equal and opposite. Hence they cancel each other. Similarly charges +q at B and E do not contribute to electric field at O. Dut to charge -q at F, the electric field at O will be E1=q4πϵ0r2 directed from O to F' This is the net electric field at O due to the five charges at A,B,C,D,E and F. The electric field at O due to charge +Q at C is given by E2=Q4πϵ0r2 we require q4πϵ0r2=2Q4πϵ0r2 which gives Q=q2. Hence the correct choice is (b).

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