Relations of Electric and Magnetic Fields. 473 



according to the so-called law of Laplace, the magnetic field 

 intensity produced at A by the element ds' ot a circular 

 conductor coincident with the concentric circle drawn 

 through P, and carrying a current of strength y = pa/a'. 

 Thus the whole magnetic field intensity F m at A, due to a 

 •current y in the concentric circle through P, is given by 



j cos# ; (V,os0 1 ^ (i) , 



•where F e is the electric (or gravitational) field intensity at 

 P due to the circle of radius a and uniform line density p. 



Of course F e is directed radially outward, while F m is 

 normal to the plane of the circles. 



The same result holds mutatis mutandis when the point P 

 is within the given circle (fig. 2). 



Kar'. 2. 



2. The mutual inductance of two concentric circles is propor- 

 tioned to the electric (or gravitational) field intensity 

 produced by a uniformly charged disk, the edge of which 

 coincides with one circle, at a point on the circumference 

 of the other. 



Imagine the charged disk divided into an infinite number 

 -of concentric narrow circular strips, and consider the out- 

 ward repulsion of each of these on unit charge at P. These 

 repulsions combine into a radially outward force at P equal 

 to their sum. But each element of repulsion is equal to the 

 product of the area of the strip producing it and the mag- 

 netic field intensity produced at any point of that strip by a 

 fixed current flowing round the other circle. This conclusion 

 seems very remarkable : 1 am not aware that it has been 

 noticed before. 



One direct mode of calculating the mutual inductance 



