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Magnetic Forces
Magnetic Field:
Magnetic Field =
B=F/qv
or
Force
SI Unit:
(charge)(speed)
F=
1T = 1N/Am
(If v and B perpendicular)
If the charge is moving as a current, I in a wire of length, L
F =
(If I and B perpendicular)
Direction of Current

Direction of Magnetic Field.
(shown lines of magnetic force)
If the field direction and charge direction are not perpendicular then
and
Note: Unlike gravitational force or electric force, magnetic force is perpendicular
to the plane formed by the field and the moving charge, and is greatest when
the magnetic field and current are perpendicular to each other. The force on
the current carrying wire shown above is therefore into the plane of the page and
is determined by using the left-hand finger rule.
. 1 G = 1 x 10-4 T
Another unit for magnetic field is
The magnetic field at the surface of the earth is about 0.5 G or 0.5 x 10 -4 T
Strong electromagnets can produce fields on the order of 2 T and
superconducting magnets over 10 T
Magnetic Field can also be defined as
Lines moving
through unit surface
area perpendicular
to the field
B = Number of Magnetic Field Lines
Area perpendicular to field
=
Flux
Area
=
/A
1 Wb = 1 T m2
Flux is measured in
Example
A synchrotron accelerates protons up to 3 x 107 m/s and uses a steering magnet
to bend them into a curved path. If the magnetic force on a proton has to be 1.9 x
10-11 N a) what strength of magnetic field is needed? b) label the direction of the
field on the diagram below and c) how much stronger is this field than the earth?
+
F
v
Electromagnetic Induction
If a current carrying wire moving in a magnetic field experiences a perpendicular
force then a changing magnetic field must induce a current in a stationary coil of
wire. So moving a magnet in and out of a wire coil must induce an alternating
current in the wire.
Faraday’s Law
If the magnetic flux (field lines) through a given area changes over time, a
voltage will be induced in the wire and a current will momentarily flow. If the
number of turns of wire is increased, the voltage will increase proportionally.
Potential difference =
(number of turns)(change in flux)
elapsed time
V = - N  / t
Lenz’s Law
The induced voltage (above) always produces a magnetic field that apposes the
field that originally produced it. This is needed to conserve energy.
Generators, Motors and Meters
When a wire in a generator coil moves through the magnetic field, free electrons
in the wire will be forced to move in a perpendicular direction. The magnitude of
the force and therefore the induced voltage thus depends on the rate at which
the wire moves through the field lines (changing flux). When the wire moves
perpendicular to the field, it will quickly cut through the field lines and the largest
induced voltage will be generated. But when the wire moves parallel to the field,
the wire will not cut through any field lines and the least induced voltage will be
generated. Similarly with a motor or coil meter, the rotating force on a current
carrying wire will change as the coil turns in the field due to a changing rate at
which the wire cuts through the field. This is why motors use multiple coil winding
orientations to maximize the turning effect (torque).
Coil cuts through field
lines (flux) at a slow rate
at the top and bottom
Coil cuts through field
lines (flux) at a fast rate
in the middle
Magnetic Forces Practice
1. In Mr. Fawcett’s TV, electron’s are shot toward the screen through a 1.0 x
10-3 T magnetic field set up in the picture tube. A) If each electron
experiences a magnetic force of 2.9 x 10-15 N, at what speed is it
propelled through the picture tube? B) How does this speed compare to
the speed of light?
2. In the giant CERN particle accelerator in Switzerland, protons are
accelerated to speeds of 2.0 x 108 m/s through a magnetic field of 3.5 T.
and then collided with a fixed target. What is the magnitude of the
magnetic force experienced by the protons as they are accelerated
around the giant ring?
3. a) What is the force per meter on a wire carrying a 7.80 A current when
perpendicular to a 0.8 T magnetic field? b) What is the angle between the
wire and field is 450 ?
4. A 10 m long section of high tension power line carries a current of 20.0 A
perpendicular to the earth’s magnetic field of 5.5 x 10-5 T. What is the
magnetic force experienced by the power line?
5. Find the direction of the magnetic force on the charges below
X
+

_
v
v
_
B
v
6. Find the direction of B for each case below.
F
+
X
v
+
v
v
X
F
_
F
7. A square coil of side 5.0 cm contains 100 loops and is positioned
perpendicular to a uniform 0.60 T magnetic field. It is quickly and uniformly
pulled from the field (moving perpendicular to B) to a region where B
drops abruptly to zero. It takes 0.1 s for the whole coil to reach the field
free region. Find the a) change in flux through the coil and b) the induced
voltage.
8. A student wears wire- rimmed glasses whose frames are shaped like two
circles each with an area of 2.0 x 10-3 m2. The horizontal component of the
earth’s magnetic field is 1.9 x 10-5 T. If the student turns her head 900 in
0.5 s, what is the induced voltage in the frame of one eyepiece?