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Question

Three point charges q1=q , q2=q and q3=Q are placed at points having position vectors r1 , r2 and (r1+r2) respectively. It is known that, |r1|=|r2|=r. The net electrostatic force on q3 is 3 times the force applied by either of q1 or q2 on q3. Find r1r2

A
r2
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B
r22
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C
r23
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D
r24
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Solution

The correct option is B r22
The positions of three point charges is as shown in the figure below,


From the data given in the question, F=3F0

From the diagram, |F1|=|F2|=F0(say)

Therefore, (F0)2+(F0)2+2(F0)cosθ=3F0

cosθ=12θ=60

So, The value of r1r2=r×r×cos60=r22

Hence, option (b) is the correct answer.

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