A coil with 300 turns is wound uniformly over a steel ring with a relative permeability of 900. The ring has a mean circumference of 400 nm and a cross-sectional area of 500 mm^2. If a current of 25 A is passed through the coil, we need to find the MMF, reluctance, and flux.





The magnetic field intensity (H) can be calculated using the formula:

H = N * I / l

Where:
N = Number of turns in the coil
I = Current passing through the coil
l = Mean length of the coil

Given:
N = 300 turns
I = 25 A
l = mean circumference of the ring = 400 nm

Substituting the given values, we get:

H = 300 * 25 / 400 = 18.75 A/m

So, the magnetic field intensity (H) is 18.75 A/m.



The magnetic flux density (B) can be calculated using the formula:

B = μ * H

Where:
μ = Permeability of the material
H = Magnetic field intensity

Given:
μ (relative permeability) = 900
H = 18.75 A/m

Substituting the given values, we get:

B = 900 * 18.75 = 16875 T

So, the magnetic flux density (B) is 16875 T.



Reluctance (R) is a measure of how difficult it is for magnetic flux to flow through a material. It can be calculated using the formula:

R = l / (μ * A)

Where:
l = Mean length of the coil
μ = Permeability of the material
A = Cross-sectional area of the coil

Given:
l = mean circumference of the ring = 400 nm
μ (relative permeability) = 900
A = 500 mm^2

Substituting the given values, we get:

R = 400 * 10^-9 / (900 * 500 * 10^-6)

R = 0.0008889 A/Wb

So, the reluctance (R) is 0.0008889 A/Wb.



Magnetomotive force (MMF) is the driving force that produces magnetic flux. It can be calculated using the formula:

MMF = H * l

Where:
H = Magnetic field intensity
l = Mean length of the coil

Given:
H = 18.75 A/m
l = mean circumference of the ring = 400 nm

Substituting the given values, we get:

MMF = 18.75 * 400 * 10^-9

MMF = 0.0075 A

So, the magnetomotive force (MMF) is 0.0075 A.