ELECTRICAL METHODS 605 



system. The coil should be tuned to the frequency, or a harmonic, of the 

 energizing power. 



Field Due to a Circular Loop at a Point on the Axis of the Loop. — 



The field due to a circular circuit of one turn at a point P (Figure 

 379) on the axis of the circle at a distance x from the center may be 

 calculated readily as follows : t 



Fig. 379. — Sketch illustrating field dH due 

 to the current element dl. 



Consider first the field dH due to the current element AB. From 



Ampere's law (Equation 1), 



,-.- Idls'md 

 dH = 5 



where dl = AB and Q equals the angle between dl and r. This field is 

 perpendicular to dl and r. Hence, sin ^ = 1. Also, from the geometry of 

 the figure, dl = a da. Hence, 



aJri — — 5 — 

 From symmetry the resultant field is along the x axis and is equal to 



or 



It is obvious that if the circular circuit has N turns, the last formula 

 would become 



"- {a'^ + x^y^ ^^^^ 



Mutual Inductance Between Parallel Coils. — The mutual induc- 

 tance M between two electrical circuits is equal to the magnetic flux 



t L. Page and N. I. Adams, Principles of Electricity, p. 247 (Van Nostrand Company, 1931). 



