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Magnetic PotentialDefinition of magnetic potential.  The magnetic potential at any point is the work done against the magnetic forces in bringing up a unit magnetic pole from the boundary of the magnetic field to the point in question.
Let us suppose that we can draw an equipotential surface belonging to a certain configuration of magnets, and that we know the strength of the magnetic field at each point of the surface. Take a small element of area, a square centimetres in extent, round any point, and through it draw lines of force in such a manner that if H be the strength of the magnetic field at the point, the number of lines of force which pass through the area a is H a. Draw these lines so that they are uniformly distributed over this small area. Do this for all points of the surface. Take any other point of the field which is not on this equipotential surface; draw a small element of a second equipotential surface round the second point and let its area be a' square centimetres. This area will, of course, be perpendicular to the lines of force which pass through it. Suppose that the number of lines of force which pass through this area is n', then it can be proved, as a consequence of the law of force between two quantities of magnetism, that the strength of the field at any point of this second small area a' is numerically equal to the ratio n'/a'. The field of force can thus be mapped out by means of the lines of force, and the intensity of the field at each point determined by their aid. The intensity is numerically equal to the number of lines of force passing through any small area of an equipotential surface divided by the number of square centimetres in that area, provided that the lines of force have originally been drawn in the manner described above.^{(1)}


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