# Magnetic Field of a Bar Magnet

• Zeophlite
In summary, the conversation discusses the creation of a simulation to understand electromagnetics using a stationary bar magnet and a moving electron. The force applied to the electron is calculated using the Lorentz force law, but the calculation of the magnetic field (B) is still unknown. The Biot-Savart law is mentioned, but it is not applicable to a bar magnet without current. Instead, the magnetic scalar potential can be used, assuming a constant magnetic density (m) over the pole surfaces. The resulting magnetic field is then dependent on the permeability of vacuum (μ0) and the relative permeability of the magnet (
Zeophlite
So I'm making a simulation to help me understand electromagnetics.
Basically I have a stationary bar magnet, along with a moving electron.
Each frame the electron has a force applied to it via the Lorentz force law, F = q(E+v cross B).
Now E = 0, but how do I calculate B?

The Biot-Savart law relates to currents, but a bar magnet doesn't have any current.

Cheers

A bar magnet is like many tiny current loops. However the treatment is actually easier if you use the magnetic scalar potential (which works as long as the electron doesn't go through the current loop).

For a bar magnet with a constant magnetization parallel to the magnet you can calculate the magnetic scalar potential by assuming that there is a constant magnetic density m spread over both the pole surfaces. Each magnetic density bit contributes
$$\mathrm{d}V_m=\frac{m\mathrm{d}A}{4\pi r}$$
(where dA is a surface element) to the scalar magnetic potential. The magnetic field from this potential - once you have summed over both pole surfaces - is
$$\vec{H}=\frac{\vec{B}}{\mu_0\mu_r}=-\nabla V_m$$

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Hello, it is great to hear that you are using simulation to understand electromagnetics. The magnetic field of a bar magnet can be calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current flowing through a wire and inversely proportional to the distance from the wire. In the case of a bar magnet, the current is essentially a collection of tiny moving charges within the magnet, which generates a magnetic field around it. This field can be calculated by considering the magnetic moments of these charges and using the Biot-Savart law. Alternatively, you can also use the magnetic dipole moment of the bar magnet to calculate the magnetic field. I would recommend researching more about magnetic dipole moments and their relationship to the magnetic field to better understand how to calculate the magnetic field of a bar magnet. Good luck with your simulation!

## 1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges or magnetic materials, such as a bar magnet.

## 2. How is the magnetic field of a bar magnet created?

The magnetic field of a bar magnet is created by the alignment of its magnetic domains. These domains are tiny regions within the magnet where the magnetic moments of individual atoms are aligned in the same direction.

## 3. How does the strength of a magnetic field vary with distance?

The strength of a magnetic field decreases as you move further away from the magnet. This relationship is described by the inverse square law, which means that the strength of the magnetic field decreases by the square of the distance from the magnet.

## 4. How can I visualize the magnetic field of a bar magnet?

You can visualize the magnetic field of a bar magnet using iron filings. When sprinkled around the magnet, the filings will align with the magnetic field lines, giving you a visual representation of the field.

## 5. What factors affect the strength of a bar magnet's magnetic field?

The strength of a bar magnet's magnetic field is affected by its size, shape, and the material it is made of. Increasing the size and strength of the magnet or using a material with a higher magnetic permeability can increase the strength of the magnetic field.

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