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# Magnetic Force

by Ron Kurtus (updated 30 May 2023)

The equation for the*of attraction or repulsion between two magnets is highly complex. However, it can be approximately expressed with a simple equation and can show the relationship with the separation of the magnets.*

**magnetic force**Likewise, the force relationship between a magnet and piece of iron can be taken from the equation.

Questions you may have include:

- What is the magnetic force equation?
- What is the force with respect to separation?
- What is the force on a piece of iron?

This lesson will answer those questions. Useful tool: Units Conversion

## Force equation

The equation for the force between two magnets can be quite complex. However, it can be simplified by considering the poles of the magnets as single points, as opposed to having distinct areas. The following equation is a good approximation of the attraction or repulsion force between the magnets:

F = pq_{1}q_{2}/4πR^{2}

where

**F**is the force in newtons (N)**p**is the magnetic permeability of the intervening medium in Tesla-meters/ampere (T-m/A), henry/meters (H/m), or newton/ampere squared (N/A^{2})**q**and_{1}**q**are the magnitudes of magnetic poles in ampere-meters_{2}**π**is the Greek letter pi (**π**= 3.14)**R**is the separation in meters

The permeability of a vacuum is **p = 4π*10 ^{−7}** H/m. The permeability of air is somewhat larger.

Notethat this equation is similar to that for the gravitational force:

F = GMm/R. (^{2}See Universal Gravitation Equation.)

## Force with respect to separation

What this means is that if everything is kept the same, the force of attraction or repulsion between two point magnetic poles with respect to their separation is:

F = k_{}/R^{2}

where **k** is some constant value.

In other words, as the magnetic poles get closer, the attraction or repulsion varies is the inverse of the separation squared. Thus, the force at 1 cm is 4 times the force at 2 cm:

F = k/1 = 4k/2^{2}

## Magnet attracts piece of iron

Once a magnetic force acts on a piece of iron, the piece temporarily acts as a magnet with the opposite pole facing the magnet's pole.

The equation **F = pq _{1}q_{2}/4πR^{2}** holds, and the force of attraction is proportional to the inverse of their separation:

F = k_{}/R^{2}

Of course, this is an approximation, but it can be used in various applications.

## Summary

The magnetic force of attraction or repulsion between two magnets can be approximated with a simple equation. This can show the force relationship of the magnets as the inverse of the separation squared.

Likewise, the force relationship between a magnet and piece of iron can be taken from the equation.

Learn as much as you can and apply your knowledge

## Resources and references

### Websites

**Force Between Magnets** - Wikipedia

### Books

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## Students and researchers

The Web address of this page is:

**www.school-for-champions.com/science/
magnetic_force.htm**

Please include it as a link on your website or as a reference in your report, document, or thesis.

## Where are you now?

## Magnetic Force