This document summarizes the motion of charged particles in a uniform magnetic field. It describes how electrons will travel in a circular path with constant speed due to the perpendicular force exerted by the magnetic field. It then provides the equations for calculating the radius, frequency, and period of the circular motion. It also discusses how a proton would travel in a circular path due to the parallel force from the magnetic field. Finally, it briefly mentions that a particle with velocity components both parallel and perpendicular to the field would follow a helical path.

1. Motion of a Charge Particle in
Uniform Magnetic Field
By Syed Mudassir Zaidi

2. Example: an electron travels at 2x107 m/s in a plane
perpendicular to a 0.01 T magnetic field. Describe its path.
Motion of a charged particle
in a uniform magnetic field

3. Example: an electron travels at 2x107 m/s in a plane
perpendicular to a 0.01 T magnetic field. Describe its path.
The above paragraph is a
description of uniform
circular motion.
The electron will move in a circular path with a constant speed
and acceleration = v2/r, where r is the radius of the circle.
The force on the electron
(remember, its charge is -) is
always perpendicular to the
velocity. If v and B are
constant, then F remains
constant (in magnitude).
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B
v
F
v
F
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4. Motion of a proton in a uniform magnetic field
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Bout
v
FB
+ +
v
v
FB
FB
r
The force is always in the
radial direction and has a
magnitude qvB. For circular
motion, a = v2/r so
The rotational frequency f is
called the cyclotron frequency
The period T is
2
mv
F = q vB =
r
q rB mv
v = r =
m q B
π π
2 r 2 m
T = =
v q B
π
q B
1
f = =
T 2 m
Thanks to Dr. Waddill for the use of the picture and following examples.
Remember: you can do
the directions “by hand”
and calculate using
magnitudes only.

5. Helical motion in a uniform magnetic field
If v and B are perpendicular, a
charged particle travels in a circular
path. v remains constant but the
direction of v constantly changes.
If v has a component parallel to B,
then v remains constant, and the
charged particle moves in a helical
path.
v
v
B
+
There won’t be any test problems on
helical motion.
*or antiparallel

6. Electrons confined to move in a plane
Thanks to Dr. Yew San Hor for this and the next slide.
Apply B-field perpendicular to plane

7. Apply B-field perpendicular to plane
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8. Lorentz Force Law
If both electric and magnetic fields are present,  .

F = q E+v B
Applications
See your textbook for numerical calculations related the next
two slides.
If I have time, I will show the mass spectrometer today.
The energy calculation in the mass spectrometer example is
often useful in homework.