Question

A particle A of mass m and charge Q moves directly towards a fixed particle B, which has charge Q. The speed of A is v when it is far away from B. The minimum seperation between the particles is proportional to

• A. $Q^2$
• B. $\frac{1}{v^2}$
• C. $\frac{1}{v}$
• D. $\frac{1}{m}$

Answer 1

Answer: (A), (B), (D)

$\frac{1}{v^2}$
$\frac{1}{m}$
$Q^2$

By conservation of energy minimum separation $\left(x_{min}\right)$ will occur when the potential energy or interaction energy in between A and B is equal to the kinetic energy of the system.
i.e, $k\frac{Q^2}{x_{min}}=\frac{1}{2}m{v}^2$ where $k=\frac{1}{4\pi {ϵ}_0}$
or $x_{min}=\frac{2k{Q}^2}{m{v}^2}$
thus, $x_{min}\propto Q^2,\frac{1}{m},\frac{1}{v^2}$