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

In summary, the conversation discusses the calculation of the magnitude of the magnetic field produced by the motion of an electron in a hydrogen atom at a distance of 5.29E-11 m with a speed of 2.19E6 m/s. The Biot-Savart's law is used with the equation dB = (u/4pi*r^2) I ds x r(roof) to calculate the magnitude of the magnetic field, with the final expression being \frac{\mu_{0}}{4\pi} \frac{ev}{r^2}. The individual arrives at a solution of 1.99 T, but the correct answer is 12.5 T, which is determined to be due to an
  • #1
cryptoguy
134
0

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.
 
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  • #2
There's one more 'r' in the denominator. The final expression is

[tex]\frac{\mu_{0}}{4\pi}[/tex] [tex]\frac{ev}{r^2}[/tex].
 
  • #3


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.
 

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

1. What is the Biot-Savart law?

The Biot-Savart law describes the magnetic field produced by a steady electric current in a given space.

2. How is the Biot-Savart law used with electrons?

The Biot-Savart law is used to calculate the magnetic field produced by moving electrons, by considering the individual contributions of each electron to the overall field.

3. What is the significance of the Biot-Savart law in electromagnetism?

The Biot-Savart law is an essential tool in understanding the behavior of magnetic fields and their interactions with electric currents, which is crucial in many areas of electromagnetism such as motors, generators, and magnetic resonance imaging.

4. How do you apply the Biot-Savart law in practice?

To apply the Biot-Savart law, you need to know the magnitude and direction of the current, the distance between the current and the point where you want to calculate the magnetic field, and the direction of the magnetic field at that point.

5. Are there any limitations to the Biot-Savart law?

Yes, the Biot-Savart law is only applicable to steady currents and does not account for the effects of changing electric fields. It also assumes that the current is confined to a specific path and does not take into account the effect of electric charges outside of this path.

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