How Does Electron Movement Affect Magnetic Fields in a Hydrogen Atom?

[cryptoguy]

Homework Statement

In a model of a hydrogen atom, an electron circles the proton at a distance of 5.29E-11 m with a speed of 2.19E6 m/s. Compute the magnitude of the magnetic field that this motion produces at the location of the proton.

Homework Equations

dB = (u/4pi*r^2) I ds x r(roof) (Biot-Savart's law)

The Attempt at a Solution

I did I = e*v/(2*pi*r) where e is electron charge and v is the velocity. I got I = .00105 A. I plug in that into B = uI/(4*pi*r) = 1.99 T but the answer is 12.5 T. What am I doing wrong? Thank you.

 

[Shooting Star]

There's one more 'r' in the denominator. The final expression is

$$\frac{\mu_{0}}{4\pi}$$ $$\frac{ev}{r^2}$$.

 

[Moetasim]

I would like to first commend you for attempting to solve this problem using the Biot-Savart law. However, it seems like you have made a mistake in your calculation. The correct value for the current, I, should be 1.05E-3 A, not 0.00105 A. This is because you need to convert the speed from meters per second to meters per revolution (since the electron is making one full revolution around the proton). This can be done by multiplying the speed by the circumference of the electron's orbit, which is 2*pi*r. Therefore, the correct value for I is 1.05E-3 A, which when plugged into the Biot-Savart law, gives a magnetic field strength of 12.5 T, as stated in the answer. I hope this helps clear up any confusion and helps you to understand the correct application of the Biot-Savart law in this scenario.