Magneto motive force question

[davidcowling]

Homework Statement

A cast steel magnet has an air gap of length 1mm and an iron path of 30cm. Find the magneto motive force (MMF) necessary to produce a flux density of 1Wb/m^2. The relative permeability of cast steel is 900. Neglect any leakage or fringing effects

Homework Equations

I think these are relevant

Flux density B = mu H
Magnetic field strength H = (NI)/L
Permeance Mu = Mu0 MuR where Mu0 = 4pi *10^-7 and MuR is the relative permeability
MMF = NI

The Attempt at a Solution

i first equated flux density and magnetic field strength together to make

B = 1 = Mu * (NI)/L

i worked Mu out to be approx 1.131*10^-3

Then substituted L as 0.3metres.

this then worked out to be

NI = 0.3 * (1.131*10^-3)

NI is then 3.39*10^-4. Which is the MMF.

Is this correct? Do i have to use the air gap of 1mm for anything?

Your help is appreciated.

 

[Jhero]

Your approach is generally correct, but there are a few errors and omissions that I would like to point out.

First, you are correct in equating the flux density and magnetic field strength, but your calculation of Mu (permeance) is incorrect. The correct value should be 1.131*10^-3 m/Wb.

Next, you are correct in substituting L as 0.3 meters, but you should also take into account the air gap of 1mm. This can be done by considering the air gap as a separate component with its own permeability (in this case, Mu0), and then adding it to the overall permeance of the system. This will give you a more accurate value for your MMF.

Finally, you have correctly calculated the MMF to be 3.39*10^-4, but you have not specified the units. The correct units for MMF are ampere-turns (AT).

So, to summarize, the correct approach would be to first calculate the permeance of the iron path, which is 1.131*10^-3 m/Wb. Then, take into account the air gap by calculating the permeance of the air gap, which is 4*pi*10^-7 m/Wb. Add these two values together to get the overall permeance of the system, which is 1.131*10^-3 + 4*pi*10^-7 = 1.131*10^-3 m/Wb. Finally, multiply this value by the desired flux density of 1 Wb/m^2 to get the required MMF of 1.131*10^-3 AT.