in which, x is the angle of the deflection.
The controlling force is
ad = H
and when the needle is in equilibrium, the component ae = H sin x is equal and opposite to ac, hence
ab cos x = H sin x
from which
ab = H(sin x / cos x) = H tan x
Since ab is proportional to the current,
ab = k C = H tan x
in which k is a constant depending upon the instrument. For any other current C',