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Question

A charge Q is placed at a distance L from the charge 2q as shown in figure.

The system of three charges will be in equilibrium, if Q is equal to

A
4q
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B
+4q
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C
8q
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D
+8q
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Solution

The correct option is D +8q
Since, the system of three charges is in equilibrium, so net forces on 2q will be zero.
direction of force (F21) on 2q due to +8q will be on the left side as shown in figure. So, the direction of force F23 will be acted towards the Q, that means Q attracting charge 2q.

Q charge will be positive in nature.

Since, 2q is at equilibrium. So, from Coulomb's law,

|F21|=|F23|

k(8q)(2q)L2=k(2q)(Q)L2

Q=8q

Q=+8q

Hence, option (c) is the correct answer.

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