Question

A particle of mass 1 gm and charge $1\mu C$ is held at rest on a frictionless horizontal surface at distance 1 m from the fixed charge 2 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of 10 m from the fixed charge

• A. $60{ms}^{-1}$
• B. $100{ms}^{-1}$
• C. $90{ms}^{-1}$
• D. $180{ms}^{-1}$

Answer 1

The correct option is D $180{ms}^{-1}$

Initial separation between the charges $r_1=1m$

Initial potential energy $U_1=\frac{k{q}_1{q}_2}{r_1}=\frac{9\times {10}^9\times {10}^{-6}\times 2\times {10}^{-3}}{1}=18J$

Initial kinetic energy $K_1=0$

Final separation between the charges $r_2=10m$

Final potential energy $U_2=\frac{k{q}_1{q}_2}{r_2}=\frac{9\times {10}^9\times {10}^{-6}\times 2\times {10}^{-3}}{10}=1.8J$

Final kinetic energy $K_2=0+\frac{1}{2}m{v}^2=\frac{1}{2}\left(0.001\right)v^2=0.0005v^2$

Using energy conservation, $K_2+u_2=K_1+U_1$

$\therefore 0.0005v^2+1.8=0+18$

$⟹v=180m/s$