A point charge `q_1=9.1muC` is held fixed at origin. A second point charge `q_2=-0.42muC` and a mass `3.2xx10^-4kg` is placed on the x-axis, `0.96m` from the origin. The second point charge is released at rest. What is its speed when it is `0.24m` from the origin?

Options

A. `26 m//s`
B. `2.6 m//s`
C. `46 m//s`
D. `4.6 m//s`

Answer

A

Explanation

From conservation of mechanical energy, we have
Decrease in electrostatic potential =Increase in kinetic energy
or `1/2 mv^2=U_i-U_f=(q_1q_2)/(4piepsilon)(1/r_i-1/r_f)`
`=(q_1q_2)/(4piepsilon_0)((r_f-r_i)/(r_ir_f))`
`:. V=sqrt((q_1q_2)/(2piepsilon_0m)((r_f-r_i)/(r_ir_f)))`
`=sqrt(((9.1xx10^-6)(-0.42xx10^-6)xx2xx9xx10^9)/(3.2xx10^-4)((0.24-0.96)/((0.24)(0.96))))`
`=26m//s`