24 ADVANCED ELECTRICITY AND MAGNETISM. 



m r mr 



fw . /_ 

 &'* \~ 



pushes sidewise on the coil (to the right or left in Fig. 19), and 

 the total force F with which the magnet pole at m pushes to 

 the right or left on the coil in Fig. 19 is equal to the product of 

 three factors, namely (a) the length of wire in the coil which is 

 2irrZ, (b) the strength of the current in the coil in abamperes, 



and (c) the radial component, -^ sin 6, of the magnetic field 

 at C due to m. Therefore: 



2wr 2 ZIm 





But the force with which the pole pushes on the coil is equal and 

 opposite to the force with which the coil acts on the pole, and 

 the force with which the coil acts on the pole may be expressed 

 as mh, where h is the intensity at the pole of the magnetic 

 field due to the coil. Therefore, ignoring algebraic signs, we 

 have: 



2<irr 2 ZIm 

 mh = (,2 + ,22)3/2 



or 



in which h is the intensity at the point m in Fig. 19 of the 

 magnetic field due to a current of I abamperes in the circular 

 coil CC, Z is the number of turns of wire in the coil, r is the 

 radius of the coil, and d is the distance of the point m from 

 the plane of the coil in centimeters. 



17. Magnetic field intensity inside of a very long coil. It is 

 desired to find the intensity at the point p, Fig. 20, of the 

 magnetic field due to a very long cylindrical coil having z turns 

 of wire per centimeter of length, the current in the coil being / 

 abamperes. Let kH be the field intensity at p due to the 

 element cc of the coil, z-dx being the number of turns of wire 



