Question

Two particles of equal mass \( m \) and equal charge \( q \) are separated by a distance of 16 cm. They do not experience any force. The value of \( \frac{q}{m} \) is                (if \( G \) is the universal gravitational constant and \( g \) is the acceleration due to gravity).

• A. \( \sqrt{4 \pi \epsilon_0 G} \)
• B. \( \sqrt{\frac{G}{4 \pi \epsilon_0}} \)
• C. \( \sqrt{\frac{\pi \epsilon_0}{G}} \)
• D. \( \sqrt{4 \pi \epsilon_0 g} \)

Hint:

When two charged particles experience no force, the electrostatic and gravitational forces must balance. Use this relation to find the value of \( \frac{q}{m} \).

Answer 1

The Correct Option is A

For two particles to experience no force, the electrostatic force must balance the gravitational force. The electrostatic force is given by: \[ F_{\text{elec}} = \frac{q^2}{4 \pi \epsilon_0 r^2} \] and the gravitational force is: \[ F_{\text{grav}} = \frac{G m^2}{r^2} \] Equating the two forces for no net force: \[ \frac{q^2}{4 \pi \epsilon_0 r^2} = \frac{G m^2}{r^2} \] Simplifying: \[ \frac{q^2}{4 \pi \epsilon_0} = G m^2 \] Thus: \[ \frac{q}{m} = \sqrt{4 \pi \epsilon_0 G} \]