# How to Calculate the Magnetic Field of a Bar Magnet

Written by thomas bourdin
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A bar magnet is a bar-shaped object that produces a magnetic field. Bar magnets are objects that are magnetised for very long periods of time. Objects that contain material that can be magnetised like this are referred to as ferromagnetic materials. Calculating the magnetic field of a bar magnet is not a straightforward task, as the field strength depends on the composition of the magnet; however, useful approximations can be made to determine the magnetic field from a bar magnet.

Skill level:
Moderate

## Instructions

1. 1

Multiply the cube of the distance from the magnet (that is, multiply the distance of an object from the magnet by itself three times) by the numbers two and pi. As an example, if the distance away from the magnet is 0.3 meters, cubing this number gives 0.027 and multiplying this by two and pi gives 0.169 meters cubed (m^3). Call this result A.

2. 2

Multiply the magnetic field at the end of the bar magnet by the length of the bar magnet and the cross-sectional area of the magnet. As an example, if the magnetic field at the magnet is 1 Tesla (Tesla being a standard unit of measurement for magnetic fields), the length of the bar magnet is 0.3 meters and the cross-sectional area is 0.01 meters squared, then the resulting number is 0.003 Tesla meters cubed (T m^3). Call this result B.

3. 3

Divide result B by result A. Concluding our example, dividing 0.003 T m^3 by 0.169m^3 gives 0.018 T. This is the magnetic field of the bar magnet.

#### Tips and warnings

• The method above is an approximation that is valid if the distance r is measured from the end of the magnet, not the centre of the magnet. The specific approach to use will depend on the geometry of the magnet and the position where the field is to be measured, and can be quite complicated.

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