The Lorentz force

This is a magnet. It has a south pole and a north pole, and a magnetic field oriented from north pole to south pole. Now, three particles are moving through this magnetic field: one proton, with a positive charge; one electron, with a negative charge; and one neutron, with no charge. The particles move in three completely different ways! The neutron continues straight ahead.

The electron turns. And the proton also turns, though the other way. A particle changes direction only when acted upon by a force. The neutron continues in a straight line. So no force is acting upon it.

But the proton and the electron - the charged particles - turn. So, it is when charged particles are moving through a magnetic field that some force arises. Let’s try bringing an electron and a proton in again, from a different angle, aligned with the field lines. No. Now they are not turning.

There is no force acting on the particles. But now they veer off, but in different directions. The particles turn because they are acted upon by a force. So, a force appears sometimes when a charged particle moves within a magnetic field. But not always.

What determines whether or not the force appears? Well, when the particle is travelling parallel to the field lines, no force appears. A force appears when a charged particle crosses the magnetic field lines. We call this force the Lorentz force. There is a simple way to remember the direction of the Lorentz force.

Use your right hand. Let your thumb point in the direction of the protons’ movement. Let your fingers point in the direction of the magnetic field. Now press with your palm. You are pressing in the direction of the Lorentz force.

The right hand rule is true only if you use your right hand, and if it is a positively charged particle moving within the magnetic field. If the particle is negative, the Lorentz force is directed in the opposite direction. Now, let’s try the right hand rule. Here comes a proton through a magnetic field. Let’s pause.

In which direction is the Lorentz force oriented? The thumb should point in the direction of the proton’s movement. The other fingers in the direction of the magnetic field. Now the palm shows the direction of the force. Is this correct?

Yes, it is correct. And here comes an electron. It is negatively charged, so the Lorentz force will act in the other direction. Yes, it is also correct. The Lorentz force affects charged particles crossing the field lines in a magnetic field.

The right hand rule indicates the direction of the Lorentz force.