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Today’s agenda:
Magnetic Fields.
You must understand the similarities and differences between electric fields and field lines,
and magnetic fields and field lines.
Magnetic Force on Moving Charged Particles.
You must be able to calculate the magnetic force on moving charged particles.
Magnetic Flux and Gauss’ Law for Magnetism.
You must be able to calculate magnetic flux and recognize the consequences of Gauss’ Law
for Magnetism.
Motion of a Charged Particle in a Uniform Magnetic
Field.
You must be able to calculate the trajectory and energy of a charged particle moving in a
uniform magnetic field.
Motion of a charged particle
in a uniform magnetic field
Example: an electron travels at 2x107 m/s in a plane
perpendicular to a 0.01 T magnetic field. Describe its path.
Example: an electron travels at 2x107 m/s in a plane
perpendicular to a 0.01 T magnetic field. Describe its path.
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).
The above paragraph is a
description of uniform
circular motion.
B
       




 
 
v
 
 





F















F
       
       - v
       
The electron will move in a circular path with a constant speed
and acceleration = v2/r, where r is the radius of the circle.
Motion of a proton in a uniform magnetic field
v
  
Bout
 FB r   
v
   + 
+
FB
FB
     
v
     
   +




      
The force is always in the
radial direction and has a
magnitude qvB. For circular
motion, a = v2/r so
mv 2
F = q vB =
r
q rB
mv
v=
r=
m
qB
Thanks to Dr. Waddill for the use of the picture and following examples.
The period T is
2πr 2πm
T=
=
v
qB
The rotational frequency f is
called the cyclotron frequency
qB
1
f= =
T 2πm
Remember: you can do
the directions “by hand”
and calculate using
magnitudes only.
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.
There won’t be any test problems on
helical motion.
B
v
+
v
Apply B-field
perpendicular
Electrons
confined
to move to
in aplane
plane
Thanks to Dr. Yew San Hor for this and the next slide.
Apply B-field perpendicular to plane









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.