CLOSED CIRCUIT IN A UNIFORM FIELD. 505 



If the velocity u is so great that the action of the current is 

 equal to that of the Earth that is, that the deflection of the 

 needle in the galvanometer is 45 we shall have 



and if we take fl 2 = L, R = #. 



Hence the resistance of the circuit in question is equal to the 

 velocity with which the bridge must be uniformly moved under 

 the given conditions, in order that the action of the current 

 induced in a galvanometer of suitable dimensions may produce a 

 deflection of 45. 



527. The following experiment, suggested by Faraday, may be 

 considered as an application of the same problem. 



Suppose that two electrodes, A and B, are immersed in water 

 on the opposite edges of a river, of a canal, or of a current in 

 the sea, and are connected by a metal conductor. If u is the 

 velocity of the current, and a the distance of the electrodes, 

 under the influence of the Earth's magnetism, an electromotive 

 force equal to iSLa will be established between them, which, in a 



circuit of resistance R, will develop a current of intensity - . 



R 



The experiment is not impracticable; but, unless we could work 

 with very great values of u and a, the polarization of the electrodes 

 would no doubt make it very difficult to verify the conclusion. 



528. CLOSED CIRCUIT IN A UNIFORM FIELD. Consider a 

 closed circuit, which may be supposed plane (487), and let S be 

 its surface. Let us suppose it placed in a uniform field of in- 

 tensity F the terrestrial field, for instance and perpendicular to the 

 direction of the field. If the frame be made to turn through an 

 angle a, the variation of the flow of magnetic force is equal to 

 FS (i-cosa), and the quantity M of electricity put in motion in 

 the circuit, which we suppose has the resistance R, is given by 

 the ratio 



FS(i -cos a) 



- 



If the frame turns through 180, face for face, we have 



