Two fixed, equal, positive charges, each of magnitude `5xx10^-5` coul are located at points A and B separated by a distance of 6m. An equal and opposite charge moves towards them along the line COD, the perpendicular bisector of the line AB.
The moving charge, when it reaches the point C at a distance of 4m from O, has a kinetic energy of 4 joules. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.

Explanation

The kinetic energy is lost and converted to electrostatic potential energy of the system as the negative charge goes from C to D and comes to rest at D instantaneously.
Loss of K.E. = Gain in potential energy
`4=U_f-U_i`
or, `4[(q.q)/(4piepsilon_0(6)^(2))+(2(q-q))/(4piepsilon_0sqrt(9+x^2))]`
`[(q.q)/(4piepsilon_0(6)^(2))+(2(q-q))/(4piepsilon_0sqrt(9+16))]`
or, `4=(2q^2)/(4piepsilon_0)[1/5-1/(sqrt(9xxx^2)]]`
or, `4=2xx(5xx10^(-5))^2xx(9xx10^(9))[1/5-1/(sqrt(9xxx^2))]`
or `4 = 9-(45)/(sqrt(9)+x^(2))`
`impliesx=sqrt(72)=8.48m`