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  4. In the diagram shown, the charge +Q is fixed. Another charge +2 q, is projected from a distance R from the fixed charge. The minimum separation between the two charges when the velocity becomes (1/√3) times of the projected velocity, is (Assume gravity to be absent)

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Q. In the diagram shown, the charge $+Q$ is fixed. Another charge $+2 q$, is projected from a distance $R$ from the fixed charge. The minimum separation between the two charges when the velocity becomes $\frac{1}{\sqrt{3}}$ times of the projected velocity, is (Assume gravity to be absent)Physics Question Image

Electric Charges and Fields

Solution:

Using conservation of angular momentum about fixed charged,
$M V \sin 30^{\circ} \times R=M v^{\prime} \times r$
$ \Rightarrow \frac{V}{2} R=\frac{V}{\sqrt{3}} r $
$ r=\frac{\sqrt{3}}{2} R$