Current produced by a single charge moving in a circlular motion

[Benkyou]

Homework Statement

In Niels Bohr's 1913 model of the hydrogen atom an electron circles the proton at a distance "R" with a speed "v". Compute the magnitude of the magnetic field that this motion produces at the location of the proton.

Homework Equations

Bio Savart

B = mu*I / 2R = mu * q * (v/2piR) / 2R

The Attempt at a Solution

The solution is stated above in the relevant equations section.

There are some misunderstandings I have as to how they arrived at the equation for the current.

First the magnetic field given by an infinite wire should be mu*I/2*pi* r but is shown as it is above without the pi in the denominator. Further, I thought that the moving charge should have a current that is equivalent to its velocity, charge, and cross sectional area ( I = nqvA ), but that is not what is correct. I feel as if I'm missing the big pink elephant in the room that is related to the period of the of charge or something. Can someone give me some help?

 

[Benkyou]

I'm sorry the magnetic field in the center of a current loop is B = mu*I / 2*R. I guess I don't understand how the current is being calculated.

 

[Redbelly98]

Current is given by

I = Q/t​

So current is due to the charge of one electron, moving in a circular loop.
To get t in the equation, how much time does it take the charge to make a complete orbit around the loop?

p.s. also, note the formula for a long straight wire does not apply here, since the current is in the form of a circular loop.

 

[Benkyou]

Current is given by

I = Q/t​

So current is due to the charge of one electron, moving in a circular loop.
To get t in the equation, how much time does it take the charge to make a complete orbit around the loop?

p.s. also, note the formula for a long straight wire does not apply here, since the current is in the form of a circular loop.

Geez I don't know why I couldn't figure it out. That makes so much sense and its so simple. I think I just need to go over the material a lot more and try to understand the concepts better. Thanks a lot I appreciate the help.