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Math Help - equipotential surfaces problem

  1. #1
    Junior Member
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    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
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  2. #2
    MHF Contributor
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    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.
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