485 PROFESSOR CLERK MAXWELL OX THE ELECTEOMAG-NETIC FIELD. 
will be increased by the following increments, 
a due to motion of conductor, 
\ dx dt ' dy dt ' dz dtr 
~r\ due 1° lengthening of circuit. 
dt \dx ds ax ds dx dsj 
The total increment will therefore be 
/dF dG\dy _ 
a \dy dx) dt a \dx dz ) dt ’ 
or, by the equations of Magnetic Force (8), 
If P is the electromotive force in the moving conductor parallel to x referred to unit 
of length, then the actual electromotive force is P a ; and since this is measured by the 
decrement of the electromagnetic momentum of the circuit, the electromotive force due 
to motion will be 
-r, dy n dz 
^—^di~^di' 
(36) 
(65) The complete equations of electromotive force on a moving conductor may now 
be written as follows : — 
Equations of Electromotive Force. 
p =H 
f dy 
-4) 
1--- 
Jdt 
1 dt 
dx 
Q=H 
( dz 
dx\ 
dG 
d F 
f dt 
-rw) 
dt 
-r | 
R=H 
dy\ 
dG 
d^ 
[y dt 
~ a dt , 
f * dt 
■ dz ' J 
The first term on the right-hand side of each equation represents the electromotive 
force arising, from the motion of the conductor itself. This electromotive force is per- 
pendicular to the direction of motion and to the lines of magnetic force; and if a 
parallelogram be drawn whose sides represent in direction and magnitude the velocity 
of the conductor and the magnetic induction at that point of the field, then the area of 
the parallelogram will represent the electromotive force due to the motion of the con- 
ductor, and the direction of the force is perpendicular to the plane of the parallelogram. 
The second term in each equation indicates the effect of changes in the position or 
strength of magnets or currents in the field. 
The third term shows the effect of the electric potential F. It has no effect in 
causing a circulating current in a closed circuit. It indicates the existence of a force 
urging the electricity to or from certain definite points in the field. 
