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EE201.3
Class Notes
Denard Lynch
Page 1 of 4
September 2007
Force on a moving charge in a magnetic field
(Note: see the last page (p4) of this section for a refresher on crossproducts if required.)
Recall the two sides of the relationship between electricity and magnetism:
i) a moving charge creates a magnetic field, and
ii) a magnetic field exerts a force on a a moving charge
We are now going to explore part ii) of this relationship.
First, highlight the differences between electric and magnetic fields w.r.t. their effect on a charged
particle:
Electric Fields
Magnetic Fields
F
e
is in the direction of the field
F
m
is perpendicular to the field
F
e
will act on a particle regardless of velocity, and
will
accelerate
a particle
F
m
only affects a charge in motion, but will
not
change
its velocity (i.e. no acceleration)
F
e
does
work
to displace/move a charge, and the
energy of the charge is affected
F
m
does
no work
on the charge, and the particles
energy is
not
affected
Recall: Work = Force acting through a distance.
F
•
d
S
=
F
•
v
dt
= 0, i.e. no work is done since there is
no force in the direction of the motion.
To explore F
m
a little further, from physics we know:
F
m
!
q
,
vel
,
B
,
where:
B
= strength of the magnetic field,
vel
is the velocity of the particle(s), and
q
is the magnitude of the charge.
Also,
F
m
is perpendicular to both
vel
and
B
.
F
m
=
q
!
vel
"
B
(1)
Now consider a collection of charged particles in a medium in the presence of a magnetic field of
concentration B.
If the charges
and
the magnetic field are
static
, there is no force or effect on the
charged particles.
However, the charged particles are all ‘drifting’ with a velocity of
v
drift
, then the
force on each one is given by (1) above, where
q
is the magnitude of the charge on one particle,
vel
is
its velocity and
B
is the density of the field.
The total number of charge carrying particles in the
medium (e.g., a wire/conductor) is equal to
nAl
, where
n
= number of particles/m
3
,
A
= crosssectional
area in m
2
, and
l
is the length of the material in m.
Then the total force (due to B) on the medium (wire) is:
F
m
!
total
=
q
"
vel
#
B
( )
nAl
( )
(2)
where
q
is the magnitude of charge per carrier in coulombs/carrier
n
is the density of the charge carriers per m
3
A
is the crosssectional area in m
2
, and
v
drift
is the velocity of the charges in m/s.
and:
I
=
qnAv
drift
(3)
F
m
B
vel
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View Full DocumentEE201.3
Class Notes
Denard Lynch
Page 2 of 4
September 2007
(Note: that all units in the expression cancel to leave coulombs/sec, and 1 c/s = 1 ampere.)
Substituting (3) into (2) results in the expression for the force on a wire in a field, B:
F
mag
=
Il
!
B
(4)
where
I
is the current in A,
l
is the length of the wire in the filed in meters, m, and
B
is the magnetic field density in Teslas, T.
Let’s look at the implication of the crossproduct or directionality.
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This note was uploaded on 09/25/2010 for the course EE 201 taught by Professor Linch during the Spring '10 term at University of Saskatchewan Management Area.
 Spring '10
 Linch

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