| − | δV | = F, − | δV | = X, − | δV | = Y, − | δV | = Z. |
| δn | δx | δy | δz |
(6)
Surfaces for which the potential is constant are called equipotential surfaces. The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles. The potential due to a single pole of strength m at the distance r from the pole is
V = m / r,
(7)
the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii. The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r′ is
V = m (l/r = l/r′).
(8)
When V is constant, this equation represents an equipotential surface.
The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis. If r and r′ make angles θ and θ′ with the axis, it is easily shown that the equation to a line of force is