# A moving charge produces a magnetic field...this happens why and how

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
A charged particle moving without acceleration produces an electricas well as a magnetic field.
Electric and magnetic fields are what theelectromagneticfield 'looks like' from a particular (inertial) frame of reference.

Take a charged particle: In its rest frame, it appears to generate an electric field only and no magnetic field at all. From a different frame of reference (in particular one in relative motion), we'll see the charge moving, thus a current which generates a magnetic field as well.

This does not mean that setting the particle in motion somehow flipped a switch within the particle - rather, it's an artifact of our choice of frame of reference: Observers in relative motion will measure different strenghts of electric and magnetic fields the same way they measure different velocities and momenta.

There are however invariants of the electromagnetic field, ie things all observers can agree upon, and in particular

PQ=B?2-E?2=E?·B?

Let's take a nonzero em field withP,Q=0, ieE?2=B?2andE??B?. An example would be a plane electromagnetic wave, which will look like a plane wave for everyone.

Now, letP?0butQ=0. Then, we can find frames of reference where either the electric (in case ofP>0) or the magnetic field (in case ofP<0) vanishes. The rest frame of our charged particle would be such a one.

Thanks & Regards

Rinkoo Gupta