Question

# Nine point charges placed at the vertices of an octagon and centre of an octagon as shown in the figure. Net force experienced by +q charge at the centre of the octagon is zero. If any two charges are removed simultaneously from the vertex, it observed that net force on charge +q is still zero, then the charges will be

A
+3Q and +2Q
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B
+Q and Q
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C
4Q and +3Q
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D
any pair of diagonally opposite charges
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Solution

## The correct option is D any pair of diagonally opposite chargesThe force experienced by the charge +q placed at the centre of the octagon is shown in the figure. Let a be the distance between centre and vertex of the octagon. So, Force on +q due to −Q, F02=F06=kQqa2 Similarly, F03=F07=k(3Q)qa2=3kQqa2; F04=F08=4kQqa2 and F01=F05=2kQqa2 Here, only diagonally opposite charges apply equal and opposite forces on +q. So, if we remove any pair of diagonally opposite charges from vertex of the octagon, net forces on +q will be unaffected. Hence, option (d) is the correct answer.

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