Classical Physics II
PHY132
Lecture 14
M
ti
II M
ti
t
Magnetism II: Magnetic torque
Lecture 14
1
03/03/2010

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B Force on a Moving Charge
Force on a Moving Charge
W ’
th
t th
ti
fi ld
B
We’ve seen that the magnetic field
– is
generated
by currents (i.e. vectors), e.g. wire:
–
and likewise
interacts
with currents and
i
h
(i
t
)
0
2
r
I
r
B
moving charges (i.e. vectors).
Thus we expect the magnetic FORCE vector
F
B
exerted on
a moving charge to depend on TWO vectors:
B
and
q
v
VECTOR PRODUCT:
F
B
=
q
v
×
B
(Lorentz Force)
– Force
F
is
perpendicular
to both
B
and
v
!
B
In a wire carrying a current
I = dq/dt
, charge
dq
in the wire
travels a short distance
d
l
in time
dt
:
dq
v
dq
=
dq d
l
/dt
=
I d
l
Th
th
t
ib
ti
t
th
t
t
l f
f
h
t i
d
l
f
–
Thus, the contribution to the total force from a short piece
of a
current-carrying wire is:
d
F
B
=
dq
v
dq
×
B
=
Id
l
×
B
(Lorentz Force)
Lecture 14
2
–
for a straight wire of length
l
in a uniform
B
field:
F
B
=
I
l
×
B
03/03/2010