Creating own Electromagnets & Calculating Forces between them

[BinaryBat2020]

So basically I’m trying to create my own electromagnets and conduct my own experiments. I’ll have an arduino microcontroller send a current into the wire that is coiled around the magnet, thus increasing the strength of the magnetic field, which in turn will touch with other magnets. I want to know how much force is required and at what distance apart to get two electromagnets to be attracted and touch one another. That’s it in a nutshell. That’s what I’m trying to experiment with. I’ve read that a lot of the data with regards to forces between magnets can be derived empirically, so I only need to know the basics.

This is what I have found to calculate the strength of a magnetic field with a current carrying wire.





But when it comes to calculating the force between 2 magnets, I find two different things…

One is the force between 2 current carrying wires...




Another is a law called Coulomb's Law...






It seems to me that these 2 formulas are trying to find the same thing; The force between two magnets. A current carrying wire essentially is a magnet because it produces its own magnetic field. Yet the formulas are different and I don’t know which one to use. Am I wrong? I’m not sure.

What formulas will I need to know to conduct the type of experimentation that I am looking for? There’s so much information out there that I’m not sure where to start. All I want is to apply different currents and have magnets touch each other, and to be able to calculate within a general range of how much force will be needed to do such.

I hope this is not too vague. Any feedback will be greatly appreciated thx. If there are any guides out there for experimenting with electromagnets or any resources that you think would be helpful to me plz link them below.

 

[John Canon]

Please don't try to dissect individual formulae. Past scientists and engineers have spent lifetimes developing and testing them. From your experiments, a good starting point would be to use your results to confirm those relationships in each formula.
Here is a good first-year lab experiment:

How to determine the strength of an electromagnet
As we know, Magnetic field is produced around a current-carrying conductor or wire. To determine the direction of the magnetic field produced by the conductor, hold the conductor in right palm, such that your thumb is pointing in the direction of current then the curled fingers will show the direction of magnetic field.

We can increase the intensity of the magnetic field by winding the wire in a helix structure over a ferromagnetic material. Atoms of iron are randomly oriented in the absence of an external magnetic field in such a way that the individual magnetic field cancels out. Under the influence of current, the atoms are forced to reorient in a particular direction which generates an intense magnetic field.

The magnetic field strength of an electromagnet is given by

B= kμ0 nI
The relationship between k and μ is given by,
μ= k μ0
Here, k is relative magnetic permeability,
n is the number of turns per unit length,
I is the current flowing through it,
μ0 is the permeability of free space,
μ is the permeability of material.

Relative permeability
The magnetic permeability of most of the materials is very close to the magnetic permeability of air, while the magnetic permeability of the iron or ferromagnetic materials are very high. The term which compares the ability of the material to become magnetized to the air’s magnetic permeability is known as relative permeability. If the value of it is more than one, then it shows that the material is more magnetic than the air.

How to increase the strength of an electromagnet
The magnetic field intensity of an electromagnet can be increased in three ways;

• By increasing the current
  By increasing the number of turns
  Using a magnetic material as a core

By increasing the current
As soon as we increase the amount of current in an electromagnet, the atoms start to align in the same direction creating an exhaustive magnetic field. The more atoms reorient themselves in the same direction; the more will be the magnetic field.
There comes the saturation point when all the particles have reoriented themselves perfectly in the same direction, beyond this point, no matter how much current you will increase, it won’t strengthen the magnetic field further.

By Increasing the number of turns
Each and every turn acts as the individual source of the magnetic field. The strength of the magnetic field generated by a wire decreases as the distance increases from it. In order to get a strong magnetic field, the number of turns should be more, and the windings must be close to each other.

Using a magnetic material as a core
The copper wires are wrapped on the magnetic material; why not on wood?
Suppose we use the wood and wrap the copper wires on it. We see that the magnetic field is not as strong as it used to be, when we have used soft iron material as a core. In Spite of having the same dimensions as the iron had, the magnetic field strength is not the same.

What’s the reason?
The physical quantity, magnetic permeability which is inherent property of material. It shows how much the material is attracted by the magnetic field. Roughly, we can say that the more the material is conductive, the more its magnetic permeability.

The ferromagnetic material allows the passage of magnetic flux through it, while materials like wood which is non-conductive, do not allow passage of it. Hence, when we use the soft iron core, it gets magnetized as it allows the magnetic field and becomes a temporary magnet until the current is passed through the coil.

Problem 1An electromagnet has a core of material of magnetic permeability 6.3 *10-3 H/m. The number of turns is 1000 per meter. A current of 2A flows through the solenoid. Find magnetic field intensity in core.
Solution:-
Given,
μ= 6.3*10-3 H/m
n = 1000 turns per metre
I = 2 A
B=kμ0nI
As we know, μ= k μ0, Hence
B= 6.3*10-3*1000*2
B= 12.6 N/A m

Problem 2An electromagnet has a core of relative magnetic permeability 4000 and the number of turns is 500 per meter. Calculate the magnetic field intensity when current of 10A flows through it.
Solution:-
Given,
k= 4000
n = 500 turns per meter
I = 2 A
B=?
As we know, the magnetic field intensity is given by B=kμ0nI
B= 4000*4π*10-7*500*10
B= 251.2 N/Am