Help understanding coil magnets

[algorithm]

This might seem like a breaking bad meme at first glance but its not. Im going to ask for patience as I learn in strange ways and am mathematically ignorant. But have a calculator.

Im trying to understand magnetism in coils. It seems so beyond my scope of understanding. But I believe it could be put in a way that I could wrap my noggin around (at least more easily).

So my first question is, how would I most easily go about calculating magnetism on a coil?

Say I know the weight of a external magnetic object, how could I calculate the coil turns to lift that object? And how would I determine how much impedance for the coil to perform that?

Is there a way to calculate the energy exerted on the object by the coil?

How can I calculate where the coil saturation point is?

I would much rather calculate than just wind inefficiently through trial and error and hope.

Physics seems like quite a complex field.
Although I basically just want to know how to wind a coil specifically around magnetic field on object by weight/size?

Thanks in advance.

[Picuino]

I think the question is too generic. Perhaps with a more specific problem it would be easier to answer.

A magnet does not have a constant force of attraction. It depends on the distance.

The saturation of the coil depends on the material used as the core.

[gbaddeley]

I suggest that you do some reading and come to grips with the math. In a nut shell, the force on the object is proportional to current times turns. Current is the applied voltage divided by resistance. Resistance is related to number of turns, cross section area of the wire and the geometry of the winding. The force depends on the core material, size and distance from object. As you can see there are many  variables. Build a solenoid and do some experiments with changing various aspects.

[radiolistener]

I know the weight of a external magnetic object, how could I calculate the coil turns to lift that object?

It depends on magnetic flux density of magnet core, it's size and distance to the object.

So my first question is, how would I most easily go about calculating magnetism on a coil?

For a seed, let's take a simple single layer solenoid with the following parameters:

N - coil turns count
w - coil length (meters)
D - coil diameter (meters)
n = N / w = winding density (turns per meter)

The solenoid is connected to the electric current source with the following parameters:

I - current (Amps)

Now let's calculate magnetic field strength H and magnetic flux density B:

H = n * I  [Amps/m]

B = µ0*µ * H * w/sqrt(4 * (D/2)^2 + w^2)  [Tesla]

where
µ0 = 1.25664e-06  [H/m]  (magnetic permeability of free space constant)
µ = 1    (relative magnetic permeability of solenoid core, for air=1)

And how would I determine how much impedance for the coil to perform that?

First lets calculate inductance, it is more complicated, you can estimate it with this formula:

L = (µ0*µ * D * (N^2)/2)*(ln(1+(pi*D/(2*w)))+(1/(2.3004+3.437*(w/D)+1.7636 * (w/D)^2 - (0.47/((0.755+D/w)^1.44)))))  [H]

Now you can calculate reactance:

X = 2 * pi * f * L  [Ω]

where
f = frequency (Hz)

Impedance also needs wire AC resistance. In order to calculate it, you're needs to take into account skin effect at frequency f. I'm not sure how to calculate it properly for a coil, so let's try to approximate it with a straight wire.

Rac = ρ * h / Aeff  [Ω]

where
h = pi * D * N  [meters]  (wire length)
ρ = 1/σ  [Ω/m]  (resistivity of the conductor)
σ = 5.96e7  [S/m]  (conductivity of the conductor, for Copper=5.96e7)
Aeff = δ * pi * d [m^2]  (effective cross sectional area of wire used at frequency f)
d = diameter of the conductor  [meters]
δ = sqrt( ρ / (pi * f * µ0*µc) ) [meters]   (nominal depth of penetration for a conductor at frequency f)
µc = 0.999994 [H/m]  (relative magnetic permeability of the conductor, for Copper=0.999994)

Now you have impedance of the coil:

Z = Rac + jX  [Ω]


If you just want to estimate coil resistance for DC current, you can do it a little easier:

Rdc = ρ * h / A  [Ω]

A = pi * (d/2)^2  [m^2]   (cross-sectional area of wire)

How can I calculate where the coil saturation point is?

Saturation is not a coil property, this is a property of core material and you're needs to check material datasheet to get magnetic flux density for saturation.

[GlennSprigg]

'Radiolistener' 's answer is great. However, if you need something simpler to grasp, try looking at this page, about electromagnet forces...
https://sciencing.com/calculate-force-electromagnet-5969962.html      (There are many others).
Keep in mind that as stated, there are many other factors!!  Like surface-area etc etc too.

[timenutgoblin]

Is there a way to calculate the energy exerted on the object by the coil?

Physics seems like quite a complex field.
Although I basically just want to know how to wind a coil specifically around magnetic field on object by weight/size?

Thanks in advance.

When lifting an object using a magnet in this case something made of iron or steel i.e., ferrous material, you need to consider Newton's Laws of physics. F = mg where m is the mass of the object and g is gravity (-9.81m/s²). The force of attraction between the coil and the object needs to be greater than the magnitude of the gravitational force acting on the object for the coil to lift the object off the ground/table/bench etc.

In order to levitate or suspend an object in midair you need to provide an upwards (positive) magnetic force of attraction to cancel out the downwards (negative) gravitational force acting on the object.

A useful method to determine the magnetic force of attraction of the coil would be to use kitchen scales sensitive enough to measure 1g of mass. Place the object on the scales and tare the reading so it reads zero. Then introduce the energized coil and watch the reading on the scales. Also measure the height of the coil above the object while reading the scales. The reading on the scales will go negative as the energized coil pulls upwards on the object. You can calculate the upwards force by multiplying the reading (convert to kg first) on the scales by gravity (-9.81m/s²).

The energy exerted (or work done) on the object is E = Fd. E is energy (Joules), F is force (Newtons) and d is distance between the centres of the coil and the object.

[timenutgoblin]

The energy exerted (or work done) on the object is E = Fd. E is energy (Joules), F is force (Newtons) and d is distance between the centres of the coil and the object.

I realize there is an error in my wording here. The distance is the height that the object has been lifted off the ground, not the "distance between the centres of the coil and the object."

The work done on the object lifting it above the ground should be equal to the gravitational potential energy of the object: E_p = mgh.