Lesson: Motion of Charged Particles in Uniform Magnetic Fields Physics • 9th Grade

In this lesson, we will learn how to determine the magnetic forces on charged particles in uniform magnetic fields and the motion produced by these forces.

Lesson Plan

Students will be able to

model an electric current as a one-dimensional beam of charged particles by using the equation , where is the current, is the charge of a particle, is the velocity of a particle, and is the number of particles in a length of the beam,
combine the equation with the equation to obtain the force on a single electrically charged particle moving freely in a uniform magnetic field, ,
recognize that as the direction of the instantaneous magnetic force on a freely moving charged particle in a uniform magnetic field is perpendicular to the direction of the instantaneous velocity of the particle, the particle will follow a circular path within a uniform magnetic field,
relate the equation of the centripetal force on a particle to the magnetic force equation to show that and hence, that .

Lesson Worksheet

Q1:

A particle has a charge of 160 µC. The particle enters a region containing a 420 mT uniform magnetic field, moving in the -direction at 360 m/s and in the -direction at 250 m/s, as shown in the diagram.

Calculate the magnitude of the force that acts on the particle at the point where it enters the field. Answer to two significant figures.

At what counterclockwise angle from the positive -direction in the -plane does the force act? Answer to the nearest degree.

Q2:

An electron is traveling at 3,250 m/s when it enters a 1.25 T magnetic field that is directed perpendicularly to the direction of the electron’s motion. Find the displacement of the electron from the point it enters the magnetic field to the point where its velocity is at a right angle to the direction of its velocity when it entered the field. Use the value C for the electron charge and the value kg for the electron mass. Give your answer in scientific notation to two decimal places.

Q3:

An electron is traveling at 5,700 m/s when it enters a 3.5 mT uniform magnetic field that is directed perpendicularly to the direction of the electron’s motion. Find the radius of the electron’s path. Use the value C for the electron’s charge and the value kg for the electron’s mass. Answer in scientific notation to one decimal place.