YEEDET’S CONSTANT IN ABSOLUTE UNITS. 
11 
density unity spread over a hemisphere bounded by the circle. Expanding this, we 
obtain in Art. 695 the expression for the potential of a point outside the circle, 
=z si* sm a 
^Q'.WQ,W+&c.+ji [ 
. Q!i(a)Qi(0 
( 8 ) 
where a and 6 are the angles in Art. 694. 
Let xy be the plane of the coil; then the force perpendicular to it is obtained by dif- 
ferentiating the potential with regard to z, and 
z=.r cos d=rp>j. 
Then for the force we get, changing the independent variables from r, to x, y, z, 
dad duo' dr dad dp 
dz dr ‘ dz~^~ dp ’ dz ’ 
(9) 
and remembering that 
r=\/ x 2 +y 2 +z 2 , d — — yj. 
0 , ==, and 
dz r 2 r v r y ’ 
1 v^+r+^ 
dad dad 1 dad 
( 10 ) 
But when, as in this case, the point where the potential is required is in the plane of 
the coil, we have a and 6 each = „, which gives ^=0, and reduces the expression (10) to 
Force perpendicular to plane of coil=^-=^ . ^ (11) 
Now by Art. 694, p. 301, 
|.Q i (9)=Q/(fl). 
( 12 ) 
The values of this are given in Art. 698, and in them we must put ^=0. 
Hence the force for one winding is 
dad_ 
dz 
+ &c. 
(13) 
This is the force exercised by one winding of radius con a imit magnetic pole in its 
plane distant r from its centre, when the winding carries a unit current. 
c 2 
