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PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
Moving conductor. 
§ 15. When the conductor is moving in any manner, the parts of the electromotive 
force due to the motion are, in the directions of the three axes, respectively equal to 
yl )— fiz, olz — yx, fix — ay. 
The form of these expressions shows that, when it is desirable to resolve the 
electromotive force in any other directions at right angles, the components will be 
yY-fiW, aW-ytJ, fiJJ-aV .(l) 
a, fi, y being the components of magnetic force, and U, V, W the components of 
velocity in these directions. When the motion of the body is uniform, as when it is 
revolving uniformly round an axis, and when it is symmetrical about this axis, the 
electric state may after a certain time be supposed to have become constant; there is 
then no variation of electric displacement at each point of space, and the currents of 
conduction become the total currents. We have then 
and therefore 
u = aM=-.f 
df dg 
Ix'cly 
dh 
dz 
0 . 
(2) 
There is thus no free electricity in the substance of the conductor, though there 
may be electric potential : and the normal component of the current across the surface 
of the body is zero : that is to say, 
mv=0 .(3) 
It is to be noted here that we are here dealing with the state of definite points of 
space : these are invariable. The different parts of the conductor take different 
conditions as they move from one point of space to another. 
Since the currents are confined to the conductor the vector potential due to them 
and its differential coefficients will all be continuous on passing across the surface of 
the conductor. 
With these preliminary observations we proceed to the consideration of a solid of 
infinite extent and thickness bounded by a plane face, revolving round an axis normal 
to its face. 
