MAGNETISM AND ELECTROMAGNETICS 57 

 The field intensity or magnetic force at P is, therefore, 



/ sm 2 irrnl . 

 = J - = jr sm 6 

 a* 



m 



2irrnl 

 r 2 + z 2 



X 



r 2 + x 2 (r 2 + z 2 



dynes, 



(92) 



since 



= Vr 2 + z 2 and sin = 



V 2 + x 2 

 (E) On the axis of a long solenoid. In Fig. 47 A5 is a solenoid 



FIG. 47. Magnetic field in a solenoid. 



of length I cm. and radius r cm. If n is the number of turns in 

 the solenoid, the number of turns in the section CD of width dx 



. n 

 tojdr. 



The field intensity at p due to the section CD is by equation 

 92 



Q XX 7 VVV 



(r 2 + z 2 )t Z 



where I is the current in the solenoid. 



The field intensity due to the complete solenoid is 



i 

 cH;= I zX^dx. 



To integrate this let angle GPT = 6, then 



x = r cot 0, 



