How Does the Biot-Savart Law Apply to an Electron Orbiting a Proton?

[dekoi]

Suppose an electron orbits a proton at a distance of 'r' with speed 'v'.
How could i determine the magnitude of the magnetic field at the location of the proton?

I thought it would make sense to use The Biot-Savart Law, but i don't know where to begin:
$$dB = \frac{\mu_o}{4\pi} \frac{I ds x r}{r^2}$$
(where $$ds x r$$ is a cross product of ds and r (unit vector) )

 

[mezarashi]

You'll be doing an integration around the circumference of the orbit. The vectors ds and r will always be perpendicular so you can ignore the vector operation and focus on magnitude.

A helping relationship would be that of current and electron flow. By definition:

J = nqv

where J is the current density, n is the electron density, q is the charge, and v is the average drift velocity. Since you have only one electron, you could probably assume I = qv/C, where C is the orbit's circumference.