Mass Spectrometry: More Charges Moving through Magnetic Fields for AP Physics B & C

Practice problems for these concepts can be found at:

Magnetism Practice Problems for AP Physics B & C

A magnetic field can make a charged particle travel in a circle. Here's how it performs this trick.

Let's say you have a proton traveling through a uniform magnetic field coming out of the page, and the proton is moving to the right, like the one we drew in Figure 22.7a. The magnetic field exerts a downward force on the particle (use the right-hand rule). So the path of the particle begins to bend downward, as shown in Figure 22.7b.

Now our proton is moving straight down. The force exerted on it by the magnetic field, using the right-hand rule, is now directed to the left. So the proton will begin to bend leftward. You probably see where this is going—a charged particle, traveling perpendicular to a uniform magnetic field, will follow a circular path.

We can figure out the radius of this path with some basic math. The force of the magnetic field is causing the particle to go in a circle, so this force must cause centripetal acceleration. That is,

We didn't include the "sin θ" term because the particle is always traveling perpendicular to the magnetic field. We can now solve for the radius of the particle's path:

The real-world application of this particle-in-a-circle trick is called a mass spectrometer. A mass spectrometer is a device used to determine the mass of a particle.

A mass spectrometer, in simplified form, is drawn in Figure 22.8.

A charged particle enters a uniform electric field (shown at the left in Figure 22.8). It is accelerated by the electric field. By the time it gets to the end of the electric field, it has acquired a high velocity, which can be calculated using conservation of energy. Then the particle travels through a tiny opening and enters a uniform magnetic field. This magnetic field exerts a force on the particle, and the particle begins to travel in a circle. It eventually hits the wall that divides the electric-field region from the magnetic-field region. By measuring where on the wall it hits, you can determine the radius of the particle's path. Plugging this value into the equation we derived for the radius of the path, you can calculate the particle's mass.

You may see a problem on the free-response section that involves a mass spectrometer. These problems may seem intimidating, but, when you take them one step at a time, they're not very difficult.

Practice problems for these concepts can be found at:

Magnetism Practice Problems for AP Physics B & C