# Electromagnet force on object at some distance

• Machinia
In summary: This can be seen in the following equation:F = \frac{B^3 A}{3 \mu_0}This equation is for the field in a dipole, where the magnetic field lines are perpendicular to the axis of the magnet.
Machinia
I've searched high and low and come up with a lot of "maybes" and "could be's" and "try this" to a problem which I feel should have at least a few example calculations floating around the internet. The questions is trivial but it seems like the solution is fairly complicated. I'm not looking for an exact solution as one probably doesn't exist, but at least an approximation would be nice.

Say I have an electromagnet and some distance away from it along its axis is a highly magnetically permeable material like iron. What is the force exerted on that object by the electromagnet?

Thanks for the link but I did come across that while I was searching. The problem with that formula is it's for a closed magnetic circuit meaning the magnetic flux stays within a core material except for a small airgap. With my problem, the flux is only inside the electromagnet's core, and leaves the north pole and travels through the air back to the south pole. My example electromagnet below. The object it's applying force to would be some distance from either pole.

OK, I misunderstood your meaning. Applications, such as yours, most likely have a wide range of variables to consider.
One thing is for sure: the magnetic field density (B) is inversely proportional to the square of the distance; see Biot-Savart Law: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Biosav.html#c1
The attractive force is proportional to the B-field. So you may be able to make some findings from a known piece of metal, at closer distances, then make some predictions about behavior at further distances.

Alright so first case, let's say best case scenario. Tho object I'm lifting is the same material and diameter as the core, and is a fraction of the length of the core. In which case the force exerted on it at 0 distance would be:
$$F = \frac{B^2 A}{2 \mu_0}$$

This is the formula Wikipedia provides for the force on the core of a solenoid.

If the force is proportional to the inverse squared of the distance, then the graph would look something like:

I just need to turn that curve into a usable formula.Edit:
Thanks to you I have been finding more useful information. It looks like the field strength for a monopole drops at at a squared rate, but for a dipole like an electromagnet or magnet, it drops off at a cubed rate.

Last edited:

## 1. What is the relationship between the distance and the strength of the electromagnet force?

The strength of an electromagnet force decreases as the distance between the electromagnet and the object increases. This relationship follows an inverse square law, meaning that the force decreases four times as much when the distance is doubled.

## 2. How does the shape and size of the object affect the electromagnet force?

The shape and size of an object can have an impact on the strength of the electromagnet force. Objects with a larger surface area or those that are more conductive will experience a stronger force compared to smaller or less conductive objects.

## 3. What factors influence the strength of an electromagnet force?

The strength of an electromagnet force is influenced by several factors, including the number of turns in the wire, the amount of current flowing through the wire, and the type of core material used in the electromagnet.

## 4. Can the strength of an electromagnet force be controlled?

Yes, the strength of an electromagnet force can be controlled by adjusting the current flowing through the wire or by changing the number of turns in the wire. The type of core material used can also affect the strength of the force.

## 5. What are some real-world applications of the electromagnet force?

The electromagnet force has numerous applications in everyday life, such as in electric motors, generators, and speakers. It is also used in magnetic levitation trains, MRI machines, and particle accelerators. Additionally, electromagnets are used in industrial settings for lifting and moving heavy objects.

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