Recall that a dipole is created by a positive and negative charge separated by a distance 2d. At an arbitrary point P as shown, the potential can be found by adding the potential due to each charge. Using the distances from each charge as labeled, we find an exact expression for the potential at point P. If the point P is at a large distance from the charges compared to the separation distance between the charges, an approximation can be made for the potential. First notice that for the angle q as shown, the difference between r2 and r1 is approximately equal to 2dcosq. Also, the product r1r2 is approximately r2. Put these into the expression for the potential. Earlier, we identified 2dq as the dipole moment p. Using this notation gives a final expression for the potential at a large distance from a dipole that depends on the angle q with respect to the dipole axis. Notice that at an angle of ninety degrees, the potential is zero regardless of the distance r from the dipole. This represents an equipotential surface since the potential is the same everywhere along this line. Equipotential surfaces can be found at other locations as well. If the electric field lines are drawn for the dipole configuration, notice that at every point, the electric field is perpendicular to the equipotential lines.

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