# Magnetic field caused by one Electron ?

• Mahbod|Druid
In summary, the Biot-Savart law can still be used to calculate the magnetic field of a point charge moving at a constant velocity, with the current replaced by the appropriate equivalence. For a uniformly moving charge, the E and B fields can be calculated using Lorentz transformations. The electron has a fixed intrinsic magnetic dipole moment arising from its quantum-mechanical "spin", but its small size makes it difficult to insert into equations. The moving electron produces a magnetic field equivalent to the infinitesimal current element in the Biot-Savart law.

#### Mahbod|Druid

Hi

I have read Bio-Savar , Amper law (also maxwell) about Magnetic fields

but all of them had I
bio-savar :
B = $$\frac{[tex]\mu$$0}{4$$\pi$$
}[/tex] $$\frac{ids Sin\theta}{r2}$$

Amper :
$$\int$$ B.ds = Iin $$\mu$$0

but what about a Electron moving in a line path ? how big will be its magnetic field ? it musnt be permenent though

and what about a Electron spining around itself ? this time it must be permenant but how big what are the vectors ?

Thanks

You can still use the Biot-Savart law for a point charge. You just replace the current with the appropriate equivalence. I think the wikipedia article has the equation:

http://en.wikipedia.org/wiki/Biot-Savart_law

That's for constant non-relativistic velocity though. I can't remember the equation for an arbitrary path/velocity.

For a uniformly moving charge, you can calculate the E and B fields by starting with the E field for a stationary charge, and performing a Lorentz transformation:

http://farside.ph.utexas.edu/teaching/em/lectures/node125.html

The electron has a fixed intrinsic magnetic dipole moment, but the "spin" that it arises from is quantum-mechanical in nature.

http://hyperphysics.phy-astr.gsu.edu/Hbase/spin.html

I'm not sure how much sense it makes to insert this dipole moment into the equations for the field of a magnetic dipole, because of its small size.

http://scienceworld.wolfram.com/physics/MagneticDipole.html

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I'm pretty sure the moving electron gives you exactly the type of field you get from the infinitesimal current element of Boit-Savart. You can set up a loop anywhere along the axis of symmetry and there will be a rate of increase of electric flux through this loop. The magnetic field integrated around the loop (constant field x 2pi*r) is equal to the increase of electric flux.

## What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is produced by moving electrically charged particles, such as electrons, and can exert a force on other charged particles.

## How is a magnetic field caused by one electron?

When an electron is in motion, it creates a magnetic field around itself. This magnetic field is a result of the electron's intrinsic magnetic dipole moment, which is caused by its spin and orbital motion.

## What factors affect the strength of the magnetic field produced by one electron?

The strength of the magnetic field produced by one electron is affected by the electron's charge, speed, and direction of motion. The distance from the electron also plays a role in determining the strength of the magnetic field.

## What is the direction of the magnetic field produced by one electron?

The direction of the magnetic field produced by one electron is perpendicular to the direction of the electron's motion. This means that the magnetic field will form circles around the electron's path.

## How is the magnetic field produced by one electron used in everyday life?

The magnetic field produced by one electron is used in a variety of everyday applications, such as in electric motors and generators, speakers, and magnetic storage devices like hard drives. It is also used in medical imaging techniques like MRI machines.