Download Last lecture: Magnetic Field

Last lecture: Magnetic Field
Convenient to describe the interaction at a
distance between magnets with the notion of
magnetic field.
Magnetic objects are surrounded by a
magnetic field.
Moving electrical charges are also
surrounded by a magnetic field (in addition to
the electrical field).
A vector quantity: magnitude and direction…
The letter B is used to represent magnetic
fields.
Magnetic Field Direction
The magnetic field direction (of a magnet
bar) can studied with a small compass.
N
1
S
Magnetic Field Lines
N
1
S
Magnetic Field of the Earth
A small magnetic bar should be said to have
north and south seeking poles. The north of the
bar points towards the North of the Earth.
The geographic north corresponds to a
south magnetic pole and the geographic
south corresponds to a magnetic north.
The configuration of the Earth magnetic
resemble that of a (big) magnetic bar one would
put in its center.
Magnetic Field of the Earth
Magnetic Force
Stationary charged particles do NOT
interact with a magnetic field.
Charge moving through a magnetic field
experience a magnetic force.
Value of the force is maximum when the
charge moves perpendicularly to the field
lines.
Value of the force is zero when the charge
moves parallel to the field lines.
Strength and direction of the Magnetic
Force on a charge in motion
F
F  qvB sin 
B
+q
v
Magnetic Field Magnitude
F
B
qv sin 
Magnetic Field Units
[F] = newton
[v] = m/s
[q] = C
[B] = tesla (T).
– Also called weber (Wb) per square meter.
– 1 T = 1 Wb/m2.
– 1 T = 1 N s m-1 C-1.
– 1 T = 1 N A-1 m-1.
CGS unit is the Gauss (G)
– 1 T = 104 G.
Right Hand
Rule
Provides a convenient trick to
remember the spatial relationship
between F, v, and B.
Consider the motion of positive
charge
Direction of force reversed if
negative charge.
Example: Proton traveling in a
magnetic field.
A proton moves with a speed of 8.0 x 106 m/s through a
magnetic field which has a value of 2.5 T at a 600 location.
When the proton moves eastward, the magnetic force
acting on it is a maximum, and when it moves northward,
no magnetic force acts on it. What is the strength of the
magnetic force? And what is the direction of the magnetic
field?
V = 8.0 x 106 m/s
B = 2.5 T
F  qvB sin 




F  1.6 1019 C 8.0 106 m / s  2.5T  sin 60o
 2.8 1012 N
Northward or southward.

19.4 Magnetic Force on
Current-carrying conductor.
A magnetic force is exerted on a single
charge in motion through a magnetic field.
That implies a force should also be
exerted on a collection of charges in
motion through a conductor I.e. a current.
And it does!!!
The force on a current is the sum of all
elementary forces exerted on all charge
carriers in motion.
19.4 Magnetic Force on Current
If B is directed into
the page we use blue
crosses representing
the tail of arrows
indicating the
direction of the field,
If B is directed out of
the page, we use
dots.
If B is in the page, we
use lines with arrow
heads.
x x x x
x x x x x
x x x x x x
x x x x x
x x x x
. . . .
. . . . .
. . . . . .
. . . . .
. . . .
Force on a wire carrying current in a
magnetic field.
Bin
x x x x
x x x x x
x x x x x x
x x x x x
x x x x
I=0
Bin x x x x
x x x x x
x x x x x x
x x x x x
x x x x
I
Bin x x x x
x x x x x
x x x x x x
x x x x x
x x x x
I
Force on a wire carrying
current in a magnetic field.
x
A x
x
x
x x x x
x x x x x
x x vx x x
d
q
x x x x x
x x x x x
x x x x x
x x x x x
x
x
x
x
Fmax   qvd B  nAl 
I  nqvd A
Magnetic Field and Current
Fmax  BIl at right angle from each
other.
Force on a wire carrying current in a magnetic
field.
General Case: field at angle  relative to
current.
Fmax  BIl sin 
B
B sin 

I
Mini-Quiz
In a lightning strike, there is a rapid flow of
negative charges from a cloud to the ground. In
what direction is a lightning strike deflected by
the Earth’s magnetic field?
Reasoning:
Negative charge flow down.
Positive Current upward.
B field direction Geo South to Geo North
Answer:
Force towards the west.
I
Example: Wire in Earth’s B Field
A wire carries a current of 22 A from east to west. Assume that at this
location the magnetic field of the earth is horizontal and directed from
south to north, and has a magnitude of 0.50 x 10-4 T. Find the magnetic
force on a 36-m length of wire. What happens if the direction of the
current is reversed?
B=0.50 x 10-4 T.
I = 22 A
l = 36 m
Fmax = BIl
Fmax  BIl

 0.50  104 T
 4.0  102 N
  22 A 36m 
19.7 Motion of Charged Particle in magnetic field
Consider positively charge
´ ´ ´
particle moving in a
q
uniform magnetic field.
Suppose the initial velocity ´ v ´ ´
of the particle is
perpendicular to the
direction of the field.
´
´ ´
Then a magnetic force will
be exerted on the particle
and make follow a circular ´
´ ´
path.
´
´
Bin
´
´
F´
r
´
´
´
´
´
´
´
´
´
´
´
The magnetic force produces a centripetal acceleration.
mv 2
F  qvB 
r
The particle travels on a circular trajectory with a radius:
mv
r
qB
Example: Proton moving in uniform magnetic field
A proton is moving in a circular orbit of radius 14 cm in a
uniform magnetic field of magnitude 0.35 T, directed
perpendicular to the velocity of the proton. Find the
orbital speed of the proton.
r = 0.14 m
B = 0.35 T
m = 1.67x10-27 kg
q = 1.6 x 10-19 C
mv
r
qB
qBr
v
m




1.6 1019 C  0.35T  14 102 m
1.67 10
 4.7 106 m s
27
kg

