Question

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

Answer 1

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

So option A is correct

Step-by-step 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