Two particle of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any force. The value of $\frac{q}{m}$ is

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$\sqrt{\frac{{πε}_{0}}{G}}$

$\sqrt{\frac{G}{4 {πε}_{0}}}$

$\sqrt{4 {πε}_{0} G}$

answer is D.

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Detailed Solution

They will not experience any force if $|\vec{F_{G}}| = |\vec{F_{e}}|$

$\Rightarrow G \frac{m^{2}}{{(16 \times 10^{- 2})}^{2}} = \frac{1}{4 {πε}_{0}} \cdot \frac{q^{2}}{{(16 \times 10^{- 2})}^{2}} \Rightarrow \frac{q}{m} = \sqrt{4 {πε}_{0} G}$

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