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Three positive point charges q1,q2,and q...

Three positive point charges `q_1,q_2,and q_3` form an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with same speed maintaining angles as shown in the figure. The charge `q_1` experiences a force `f_1` due to other two charges. Similarly, `q_2` experiences a force `f_2` and `q_3`, a force `f_3`. The ratio of `f_1`:`f_2`:`f_3` is

A

`1:1:1`

B

`q_1:q_2:q_3`

C

`1:sqrt3:2`

D

This ratio cannot be calculated

Text Solution

Verified by Experts

The correct Answer is:
C
Since the charges exert force on one another that are in action-reaction pair, sum of forces `overset(rarr)f_(1),overset(rarr)f_(2),`and `overset(rarr)f_(3)` is zero. So force vectors from a triangle, as shown in the figure

Applying sinc rule, we have `(f_(1))/(sin30)=(f_(2))/(sin60)=(f_(3))/(sin90)`
or `2f_(1)=(2f_(2))/(sqrt(3))=K` (suppose)
`f_(1)=(K)/(2),f_(2)=(sqrt(3))/(2)K,f_(3)=K`
So `f_(1):f_(2):f_(3)=(1)/(2):(sqrt(3))/(2):1=1:sqrt(3):2`
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