THE MAGNETIC FIELD
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Magnets always have
two poles: north and
south
Opposite poles attract,
like poles repel
If a bar magnet is
suspended from a string
so that it is free to rotate
in the horizontal plane,
then the end of the
magnet that points
towards the north
geographic pole of the
Earth is the north
seeking pole
Thus the opposite end if
the south seeking pole
A magnet creates a
magnetic field which
represents the effect of
a magnet on its
surroundings, and is
represented
by the
r
symbol B
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The field can be
visualised by using
small iron filings
sprinkled onto a smooth
surface placed on top of
a bar magnet
The iron filings align
with the magnetic field
in their vicinity
9. Magnetism
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MAGNETIC FIELD LINES
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Notice that the filings are bunched together near the
poles of the magnets
This is where the magnetic field is most intense
This is demonstrated by drawing field lines that are
densely packed near the poles
The field weakens further away from the magnet, and
the field lines are wider apart
r
The direction of the magnetic field, B , at a given
location is the direction in which the north pole of a
compass points when placed at that location
Placing a compass near a bar magnet’s south pole will
cause the north pole of the needle to point toward the
south pole of the magnet (opposites attract)
Thus the direction of the magnetic field at that location
is towards the magnet’s south
pole
As a consequence
the magnetic field
must point away
from the magnet’s
north pole
Magnetic field lines exit from the
north pole of a magnet and enter
and the south pole
9. Magnetism
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GEOMAGNETISM
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The Earth produces its own magnetic field, similar to
that of a bar magnet, with a pole near each geographic
pole
The magnetic poles are at an incline to the rotational
axis that varies slowly with time by about 11.5°
The north pole of a compass needle points toward the
north magnetic pole of the Earth
Since opposite poles attract it follows that the north
geographic pole of the Earth is actually near the south
pole of the Earth’s magnetic field
The Earth’s magnetic field lines are horizontal (parallel)
near the equator, but enter or leave the Earth vertically
near the poles
The field is caused by the flowing
currents of molten material
in the core
The field also reverses
direction, the last of
which was 780,000
years ago
9. Magnetism
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MAGNITUDE OF THE MAGNETIC
FORCE ON MOVING CHARGES
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Here we will consider the force a magnetic field exerts
on a moving electric charger
Consider a magnetic field B that points from left to
right in the plane of this page
A particlerof charge q moves throughr this region
with a
r
velocity v , and the angle between v and B is θ
r
Thus the magnitude of the force F experienced by this
particle is given by F = │q │vBsinθ (Newtons)
The magnetic force depends on the charge of the
particle q and the magnetic field B
It also depends on the speed of the particle v and the
magnitude of the angle between the velocity vector and
the magnetic field vector, θ
A particle must have a charge and must be moving if
the magnetic field is to exert a force on it
When θ = 0 or 180° the particle moves in the direction
of the field, or opposite to it, and the force vanishes
The maximum force is experienced when the particle
moves at right angles to the field, when θ = 90°
9. Magnetism
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DEFINITION OF THE MAGNITUDE
OF THE MAGNETIC FIELD
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The magnitude, or strength, of a magnetic field is
defined by rearranging the previous equation for F
B = F/(│q│vsinθ units 1 N/(A.m) = 1 Tesla (T)
1 gauss = 1G = 10-4T
Example: Particle 1, with a charge q1 = 3.6µC and a
speed v1 = 862m/s, travels at right angles to a uniform
magnetic field. The magnetic force it experiences is
4.25×10-3N. Particle 2, with a charge q2 = 53.0µC and a
speed v2 = 1.3×103m/s, moves at an angle 55.0°
relative to the same magnetic field. Find the strength of
the magnetic field and the magnitude of the magnetic
force exerted on particle 2.
9. Magnetism
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DIRECTION OF THE MAGNETIC
FORCE
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r
Unexpectedly, the magnetic force F points
in ar
r
direction that is perpendicular to both B and v
r
r
Figure (a) shows B and v lying
in the indicated plane
The forcer on a positive
charge, F , is perpendicular
to this plane and hence
r
r
B and v
r
The direction of F can be
determined using the
right hand rule
To find the direction of the
magnetic force on a +ve
charge, start by pointing
the fingers of your right
hand in the direction of the
r
velocity v . Now curl your
fingers toward the direction
r
of B (b). Your thumb
r points
in the direction of F . If the
charge is negative, the force
points opposite to the direction
to your thumb
9. Magnetism
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MAGNETIC FORCE FOR POSITIVE
AND NEGATIVE CHARGES
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The direction of the magnetic force depends on the sign
of the charge
The force exerted on a negatively charged particle is
opposite in direction to the force exerted on a positively
charged particle
r
The magnetic field B points into the page, and a
particle with a positive charge q moves to the right
Extend your fingers to the right and curl them into the
page and thus from the RHR the force exerted is
upward
r
If the charge is negative, the direction of F is reversed
9. Magnetism
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ELECTRIC VERSUS MAGNETIC
FORCES
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A positively charged particle moving horizontally into a
uniform electric field pointing downward experiences a
constant downward force (similar to gravity)
As a result the particle accelerates downward and
follows a parabolic path
However were a positive particle were to move in a
magnetic field, the magnetic force points into the page
As a result, the particle follows a circular path
Because the magnetic force is at right angles to the
direction of motion, no work is done on it, hence the
speed of the particle in a magnetic field is constant
Recall that the magnetic force is zero if a particle’s
velocity is parallel (or antiparallel) to the magnetic field
In this case, the particle’s acceleration is zero, and thus
its velocity remains constant, and will move in a straight
line drift along the magnetic field lines
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CIRCULAR MOTION (1)
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Consider a particle of mass m, charge +q, speed v,
r
moves in a region with a constant
magnetic field B r
r
pointing out of the page and B is perpendicular to v
Thus F = │q│ vBsin90° = │q│vB
At point 1, the particle moves to the right, hence the
magnetic force is downward
At point 2, it is moving downward, and the magnetic
force is to the left
At point 3, the force is upwards and so on
At each point on the particle’s path, the magnetic force
is at right angles to the velocity, pointing toward a
common centre – the condition required for circular
motion
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CIRCULAR MOTION (2)
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In circular motion, the acceleration is toward the centre
of the circle
Thus a centripetal force is required to cause the motion
In this case, the centripetal force is supplied by the
magnetic force
Recall that acp = v2/r
If macp is equal to the magnitude of the magnetic force,
then m(v2/r) = │q│vB
Thus the radius of circular orbit is r = mv/│q│B
A mass spectrometer is used to separate isotopes
(atoms of the same element with different masses) and
to measure atomic masses
Inside such a device a beam of ions of mass m and
charge +q enter a region of constant magnetic field with
a speed v
The field causes the ions to move along a circular path,
with a radius that depends on the mass and charge of
the ion
Different isotopes follow different paths and hence can
be separated and identified
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MASS SPECTROMETER: EXAMPLE
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Two isotopes of uranium, 235U (m = 3.9×10-25kg) and
238U (m = 3.95×10-25kg), are sent into a mass
spectrometer with a speed of 1.05×105 m/s. Given that
each isotope is singly ionised and that the strength of
the magnetic field is 0.75T, what is the distance d
between the two isotopes after they complete half a
circular orbit?
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HELICAL MOTION
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Here we consider what happens when a particle has an
initial velocity at an angle to the magnetic field
In such
a case, there is a component
of velocity parallel
r
r
to B and perpendicular to B
The parallel component of the velocity remains
constant with time (zero force in this direction)
The perpendicular component results in a circular
motion
A combination of these motions causes the particle to
move in a helical path
If the magnetic field is
curved (bar magnet,
Earth), the helical
motion of charged
particles will be
curved as well
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THE MAGNETIC FORCE ON A
CURRENT-CARRYING WIRE
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Whether it travels in a vacuum or a current carrying
wire, a charged particle will experience a force when it
moves across magnetic field lines
A wire with a current will experience a force that is the
resultant of all the forces experienced by the individual
moving charges
Consider a straight wire segment, length L, with a
current I flowing from left to right
r
It is in the region of a magnetic field B at an angle θ to
the length of the wire
Charges move through the wire at an average speed v
The time taken for them to travel L is ∆t = L/v
Thus q = I∆t = IL/v
So F = qvB sinθ = (IL/v)vB sinθ = ILB sinθ (Newtons)
9. Magnetism
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THE MAGNETIC FORCE ON A
CURRENT-CARRYING WIRE:
EXAMPLE
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A copper rod 0.15m long and with a mass of 0.05kg is
suspended from two thin, flexible wires. At right angles
to the rod is a uniform magnetic field of 0.55T pointing
into the page. Find the direction and magnitude of the
electric current needed to levitate the copper rod.
9. Magnetism
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