how to measure permeability of iron core?

if wrap copper wire around an electromagnet and measure the magnetic field, and know the number of turns and current input, could i calculate the relative permeability of the iron core?

Basically yes, however you need to know the geometry of the magnetic path, average length and cross section, also length of a possible air gap. Also consider that permeability of ferromagnetic materials is non-linear and that the B = f(H) curve involves remanence (hysteresis).

How do you measure magnetic field?

i am planning to buy a magnetic sensor on the internet. i did research i can buy magnetic sensors on the internet. how do you calculate the magnetic path? i am thinking of using a rod with many turns of wire as the electromagnet.

Measure the inductance of the coil with and without the core present - the ratio of inductance is a fair measure of the relative permeability of the core - it needs to be a completely closed mag path to get the exact result - but it will give you a comparative indication ...

yes..its Amperes Law that you need..
N.I = Hdl
where
dl is the magnetic path length
H is magnetic field strength
N = no turns
I = current

Now H = B/(u0.ur)

Where B = magnetic field strength.

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You are going to struggle to measure the magnetic field inside the solid core.
If you use a rod core, then your magnetic path length will be difficult to calculate.

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Also,.....

Reluctance = l/(u(0).u(r).A)
{where:
u(0) = 4.pi*10e-7
l = length of the uniform magnetic circuit,
A = area of the magnetic core}

(the above is from the following...
https://massey276.wixsite.com/maths)

...to calculate the dims you require, you need the core datasheet.

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Also, inductance = N^2/RELUCTANCE

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So you can measure the inductance........you know the number of turns...so you can calculate the reluctance......then from reluctance and area and length, you can get your "ur"...relative permeability

i am thinking i will measure the magnetic field a few millimeters from the core and then use equations B = uH and H = N^2A to calculate relative permeability of core. will that give me an accurate value of permeability?

H=N^2.A doesnt sound right

Ampere.Turns per metre doesnt equal metre^2

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i am thinking i will measure the magnetic field a few millimeters from the core and then use equations B = uH and H = N^2A to calculate relative permeability of core. will that give me an accurate value of permeability?

Click to expand...

sorry but no, you will be measuring in the air

so there is no magnetic field present a few millimeters from the core?

There's of course a magnetic field outside the core, but no simple relation between field strength and permeability.

A classical physics lab experiment compares the inductance of two toroid coils of identical geometry, one has a non-magnetic, e.g. wooden and the other a laminated iron core.

FvM said:

There's of course a magnetic field outside the core, but no simple relation between field strength and permeability.

A classical physics lab experiment compares the inductance of two toroid coils of identical geometry, one has a non-magnetic, e.g. wooden and the other a laminated iron core.

Click to expand...

but is there any way to measure the magnetic field 3 millimeters from the core and calculate the permeability of the iron at that magnetic field? i already know increasing the magnetic field increase the relative permeability up to a maximum and then the permeability decreases.

The relation between H and B in a magnetic circuit with air gap (or long return path in air, as in your example) is described by the term "effective permeability". Unfortunately it's not proportional to core permeability. The larger the air gap the less depends the effective permeability on the core permeability.

For a simple geometry with small air gap like a gapped toroid core, effective permeability can be calculated with fair accuracy and in return, core permeability can be at least roughly estimated. But in geometry with inhomogeneous field like presently discussed, the relation can be only obtained by solving complex differential equations or more simply by finite element methods.

so if i wrap some coils around a iron cylinder and measure the the magnetic field 3 millimeters from the core, the permeability of the core can be calculated using complex differential equations or by finite element methods? just trying to make sure i understand the response.

Theoretically yes. In practice you'll having problems to determine if the permeability is 1000 or 10000, due to the previously mentioned relations. As suggested in post #4, you really should prefer a closed magnetic circuit.

what if i measure how much weight the electromagnet can lift with the iron core and then without the iron core, would that give me accurate values of the relative permeability of the iron core? i measure the weight of the metal object the electromagnet is lifting.

I think the simpler method is that suggested in #4.

The best approach depends greatly on the shape of the core, and the size/type of sensor you have. This is easiest when your core forms closed path (since that confines most of the field to a known path) except for a very small gap, and you sense the field inside that gap. Works well with toroids and E-shaped cores. If the gap is very small, you can assume you will actually be measuring the field inside the core.

For cores which don't form a closed path (like a rod), there's no easy way to do it, since all of your field lines will pass through both the core and through air. Simulation is basically the only option, and would it would take a lot of expertise to get an accurate result.

For measuring rods, one approach is to put the rod inside a yolk, so that the rod+yolk together form a closed path (again with a small gap somewhere). This will allow the core magnetic field to be measured very accurately. If the permeability of the yolk material is known, then you can analytically calculate the permeability of the rod.