The inductance is 3.4 X 10⁻³H
Explanation:
Give-
N/L = 1800turns/m
radius, r = 0.022m
N = 100 turns
We know,
Ф = BA
and
B = (N*i*u)/l
Substituting both the equations, we get
Ф = L*i/N
N / (N/l) = l
where,
l = length
L = mutual induction
substitute (N*i*u)/l for B in Ф = BA :
Ф = (N*i*μ*A)/l
set the two Ф equal to each other:
(L*i)/N = (N*i*μ*A)/l
Solve for L:
L = (N^2 X μ X A)/l
Substitute N / (N/l) for l
[tex]L = \frac{(N^2 X u X A)}{( \frac{N}{N/l} )}[/tex]
[tex]L = N X (mu) X n\pi r^2[/tex]
[tex]L = (100) X (4\pi X 10^-^7) X (1800) X \pi X (0.022)^2\\\\L = 3.4 X 10^-^3H[/tex]
Therefore, the inductance is 3.4 X 10⁻³H
