Question

A particle of mass $2g$ and charge $1\mu C$ is held at a distance of 1 m from a fixed charge $1mC$. If the particle is released it will be repelled. The speed of particle when it is at a distance of 10 metre from the fixed charge is :

• A. 90 m/s
• B. 100 m/s
• C. 45 m/s
• D. 55 m/s

Answer 1

The correct option is A 90 m/s

Potential at 1 m from the charge

$V_A=\frac{K\times {10}^{-3}}{1}$

Potential at 10 m from the charge

$V_B=\frac{K\times {10}^{-3}}{10}=K\times {10}^{-4}$

potential diff $=V_A-V_B=K({10}^{-3}-{10}^{-4})$

Its velocity at 10 m is V, then

$\frac{1}{2}\times m{v}^2=(V_A-V_B)q$

$\frac{1}{2}\times 2\times {10}^{-3}{v}^2=K\times {10}^{-6}(1-\frac{1}{10})\times {10}^{-3}$

$v^2=K\times \frac{9}{10}\times {10}^{-6}$

$9\times {10}^9\times \frac{9}{10}\times {10}^{-6}=81\times 100$

$v=90m/sec$