Magnetic field of moving charged particle

1. Jun 26, 2009

grundletaint

What is the appropriate way to model the magnetic field of a moving charged point particle?

I don't believe you can use Biot-Savart because it is not a steady current.

I am trying to figure out what EMF (current) would be induced in a square or round conducting loop when a charged point particle passes through it.

Thanks

2. Jun 26, 2009

jorgext

Maybe BS Equation help, integrating over a single point.

$$\vec{B}(\vec{r})=\dfrac{\mu_0}{4\pi}\dfrac{e (\vec{v} \times \hat{r})}{r^2}$$

3. Jun 26, 2009

Bob S

The point charged particle moving through a loop will develop an azimuthal magnetic pulse, but because there is no net magnetic flux linking the loop, there will be no induced azimuthal EMF. The magnetic field from either a point charge-current or a steady current is azimuthal, and the electric field is radial. For relativistic point charges, the longitudinal extent of the fields are collapsed by the factor gamma, so the observed pulses are very short, and very high amplitude.