# Magnetic field caused by one Electron ?

1. May 12, 2009

### Mahbod|Druid

Hi

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

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

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

2. May 12, 2009

### Born2bwire

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.

3. May 12, 2009

### Staff: Mentor

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

Last edited: May 12, 2009
4. May 12, 2009

### conway

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.