Three positive point charges $q_{1}, q_{2} a n d q_{3}$ 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 figure. The charge $q_{1}$ experiences a force $f_{1}$ due to other two charges. Similarly, $q_{2}$ experiences a force $f_{2} a n d q_{3}, a f o r c e f_{3} .$ The ratio $f_{1} : f_{2} : f_{3}$ is

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1:1:1

$1 : \sqrt{3} : 2$

$q_{1} : q_{2} : q_{3}$

This ratio cannot be calculated

answer is C.

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Detailed Solution

Since the charges exert force on one another that are in action-reaction pair, sum of forces ${\vec{f}}_{1}, {\vec{f}}_{2} a n d {\vec{f}}_{3}$ is zero.So force vectors form a triangle, as shown in the figure.

Applying sine rule, we have

$\frac{f_{1}}{\sin 30^{0}} = \frac{f_{2}}{\sin 60^{0}} = \frac{f_{3}}{\sin 90^{0}}$

or $2 f_{1} = \frac{2 f_{2}}{\sqrt{3}} = f_{3} = k (\sup p o s e)$

$f_{1} = \frac{k}{2}, f_{2} = \frac{\sqrt{3}}{2} k, f_{3} = k$

So $f_{1} : f_{2} : f_{3} = \frac{1}{2} : \frac{\sqrt{3}}{2} : 1 = 1 : \sqrt{3} : 2$

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