Calculate the reluctance of a 4-meter long toroidal coil made of low-carbon steel with an inner radius of 1.75 cm and an outer radius of 2.25 cm. The permeability of the steel is 2 x 10^-4 Wb/At - m.

A) 31.9 x 10^6 At/Wb

B) 1.96 x 10^-5 At/Wb

C) 4.03 x 10^5 AtWb

D) 2.29 x 10^6 At/Wb

R = 31.9 x 10^ (6) At/Wb

So option A is correct

Explanation:

Reluctance is obtained by dividing the length of the magnetic path L by the permeability times the cross-sectional area A

Thus; R = L/μA,

Now from the question,

L = 4m

r_1 = 1.75cm = 0.0175m

r_2 = 2.2cm = 0.022m

So Area will be A_2 - A_1

Thus = π (r_2) ² - π (r_1) ²

A = π (0.0225) ² - π (0.0175) ²

A = π[0.0002]

A = 6.28 x 10^ (-4) m²

We are given that;

L = 4m

μ_steel = 2 x 10^ (-4) Wb/At - m

Thus, reluctance is calculated as;

R = 4 / (2 x 10^ (-4) x 6.28x 10^ (-4))

R = 0.319 x 10^ (8) At/Wb

R = 31.9 x 10^ (6) At/Wb