Chapter 1

Electrostatics and Magnetostatics

Magnetic field at the center of the Hydrogen atom

Take 10 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

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An electron travels in a circle of radius around a proton.

Question

Compute the magnetic field created by the electron at the point where the proton is located.

Hint

We can use the Biot-Savart law or assume the hydrogen atom is like a circular loop of current.

Solution

The magnetic field created by the electron at the center of the nucleus is :

Newton's second law applied to the electron gives the velocity of the electron :

Hence :

We can finally deduce the magnetic field :

Numerically : .

Magnetic field at the center of an atom
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