First progress report on a multi-channel magnetic drum inner ...

and this spreading would cause a broadening of the pattern. Actually a
broadening of the dipole reflects itself very slowly in the voltage pattern,
so much so that expected deviations from a line dipole would produce effects
below the experimental error of the measurements. This can be seen by com-
paring the field produced by a line dipole of uniform strength spread over
an area. Let the dipole have a width ol 2 t^%, its center being % distance
from the origin. Then, for a given total strength of dipole we have
and hence
e = k
e a
2AX
[(tan-1 ( ^^
)
. tan-1 ( ^-^
. (tan-l it^ )
)}
- t.n-1 (^^ ))]
To find the effect of a small ^t on e we expand the first two terms in
a series about the point %-y. and the second two terms in a series about the
point X+x. To a first approximation, then
e" = k
A-3
L\(X-x)2.y^ (?:*x)2.y2/ 3y3 1(1,22)3 (u„2)3 j
where % = =^ and w = =^ . The first term of the righf-hand side is the
y y
same as the expression obtained under the assumption that the pole is a
line pole (has no breadth), so the second term shows us the effect of
broadening the pole . It shows that for A ^ = 1/4 the error produced in
e of Figure 3 is only about 1/5% at x = 1.8 and 1^ at x = 1.5.