Question

A charge $q$ of mass $m$ is released with a velocity $1\times {10}^{6}m/s$ from a large distance from a fixed positive charge $Q$. The closest distance of approach is:

• A. $\frac{9Qq}{{10}^{3}m}$
• B. $\frac{18Qq}{{10}^{3}m}$
• C. $\frac{3Qq}{{10}^{3}m}$
• D. $\frac{Qq}{{10}^{3}m}$

Answer 1

Answer: (B)

$\frac{18Qq}{{10}^{3}m}$

Apply energy conservation
Total initial energy $=$ Total final energy, where initial energy is the energy when the particle is released and final energy is the energy when the particle is at closest distance.
$\Rightarrow$ Initial kinteic energy + Initial potential energy $=$ Final kinetic energy + Final potential energy.
$\Rightarrow \frac{1}{2}m{v}^2$ + 0 ($\because$ at very large distance, potential energy is zero) $=$ 0 ($\because$ velocity is zero at closest distance) + $\frac{1}{4\pi \epsilon o}\frac{Qq}{r}$.
$\Rightarrow \frac{1}{2}m\times {10}^{12}=9\times {10}^9\frac{Qq}{r}$
$\Rightarrow r=\frac{18Qq}{{10}^{3}m}$