CHAPTER XVIII 

 SOME MAGNETIC FIELDS 



Small magnets Magnetic shells Uniform sphere. 



The potential of a small magnet at any point in its 

 field. Let ACB represent a small magnet of length I, poles m, 

 moment M = ml. Let P be a point at a distance r from its centre 

 C in a direction CP making with CA. The potential at P is 



m 



m 



~ AP~BP' 

 Draw MCN perpendicular to CP, and draw PA M, PNB. We 



'P 



FIG. 165. 



suppose CP so large compared with / that AM and BN may be 

 taken as perpendicular to MN, and PM = PN = PC. 



Then PA = PM - AM = PC - AM = r - -' cos 

 and PB = PN + NB = PC + NB = r + J cos 



;// m ml cos 



r-jcosfl r+^cos0 



M cos .I 2 

 % when we neglect -3 



219 



-| 2 cos 2 

 4 



