MAGNETIC METHODS 



81 



Fig. 16. — Magnetic force at a point due to a bar 

 magnet in any position: Position III of Gauss. 



M, the end-on magnet a moment Mi, and the broadside magnet a 

 moment M^, 



Mi — M cos a and Mz = M sin a 



This gives a combination of Cases I and II. 



.. 2 M cos a , , -.^ Msina ,^.. 

 ri,„= ;;; end on ; and H2p— ;j^ (24) 



' ip 



d^ 



d^ 



To calculate the magnitude and direction of the resulting force at P, it 

 is necessary to determine the angle yS : 



Hop iWsina ,, ,^-^ 



tan /?= 77^=^77 = U tan a (25) 



^ Hip 2M cos a '^ ^ ^ 



Magnitude of Intensity, Hp 



^ (2Mcosa)^ (Msina)2 _ ^ikf^ cos^ a + M^ sin^ a 



iW 



//p =--^V4 cos^ a + sin^ a 



(26) 



Behavior of a Magnet in a Homogeneous Magnetic Field 



In a homogeneous or uniform magnetic field, the field intensity is con- 

 stant and always in the same direction. 



A magnet free to turn in a horizontal plane will come to rest when its 

 axis is aligned with the direction of the homogeneous magnetic field in 



