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Question: Two particle of equal mass \(m\) and charge \(q\) are placed at a distance of 16 cm. They do not exp...

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

A

l

B

πε0G\sqrt{\frac{\pi\varepsilon_{0}}{G}}

C

G4πε0\sqrt{\frac{G}{4\pi\varepsilon_{0}}}

D

4πε0G\sqrt{4\pi\varepsilon_{0}G}

Answer

4πε0G\sqrt{4\pi\varepsilon_{0}G}

Explanation

Solution

They will not experience any force if

∣FG→∣=∣Fe→∣|\overset{\rightarrow}{F_{G}}| = |\overset{\rightarrow}{F_{e}}|

⇒Gm2(16×10−2)2=14πε0.q2(16×10−2)2G\frac{m^{2}}{(16 \times 10^{- 2})^{2}} = \frac{1}{4\pi\varepsilon_{0}}.\frac{q^{2}}{(16 \times 10^{- 2})^{2}}⇒ qm=4πε0G\frac{q}{m} = \sqrt{4\pi\varepsilon_{0}G}