Thread: equipotential surfaces problem

1. equipotential surfaces problem

A positive point charge is surrounded by an equipotential surface A, which has a radius of rA. A positive test charge moves from surface A to another equipotential surface B, which has a radius rB. In the process, the electric force does negative work.

The positive point charge is q = +7.5 10-8 C, and the test charge is q0 = +6.0 10-11 C. The work done by the electric force as the test charge moves from surface A to surface B is WAB = -8.1 10-9 J. The radius of surface A is rA = 1.7 m.

Find rB, the radius of surface B.

Could someone help me set this problem up. I hit a wall and don't know what to do

Thanks

2. From Wikipedia: "The electric potential created by a point charge q, at a distance r from the charge (relative to the potential at infinity), can be shown to be $V_\mathbf{E} = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$." Since the potential is the potential energy of the test charge divided by the test charge itself, you know the energy of the test charge at $r_A$. Similarly, you know the energy of the test charge at $r_B$ as an expression of $r_B$. Finally, you know the difference of these energies, which is the work done by the electric force. From here, you can find $r_B$.