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

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Solution

The correct option is **D** any pair of diagonally opposite charges

The 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.

The 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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