Mirrors of Magnetism. 221 



The total potential at C is therefore . 



r n r 2 



If we choose C at a point of zero potential, we have 



r x r 2 ' 

 that is to say 



m 2 r 2 ' 



but — is a constant; therefore, if we take C at the points of 

 m 2 



zero potential — will always be constant. But if a point 



moves so that — remains constant it moves on the surface of 



a sphere, therefore the equipotential surface of value zero is 

 in the form of a spherical shell. If be the centre of the 

 sphere, it follows from a well-known property of a circle that 



AO __ ri m^ 



06 r 2 m 2 



If, therefore, we are given m 1 we can find from the equation 







m 2 =zm 1 j^ ) 



the strength of pole m 2 which when placed at B will give 

 zero potential on a given spherical shell. 



Now consider a magnet pole +>fti (fig. 13) brought up to 



a point A near a sphere of very susceptible material whose 

 radius is large as compared with the distance between A and 

 its surface, so that we may neglect the potential of the sphere 



