Chapter 21
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Magnets, as you know, can exert forces on
one another.
In electricity, we talk about negative and
positive dipoles or charges.
In magnetism, we discuss north and south
poles.
Like poles repel each other, and unlike poles
attract.
ELECTRIC CHARGES
MAGNETS
Can be positive or negative
Positive and negative
charges can be separated
so that a (+) or (-) charge is
isolated.
 Produce an electric field
that is a vector quantity
 Electric field points away
from positive and toward
negative
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Have a negative end and a
positive end.
ALL MAGNETS have a negative
and positive or north and south
end.
Produce a magnetic field that is
a vector quantity
Magnetic field direction is
determined by the direction of
the north pole of a compass at a
particular point
Lines tend to originate at north
and end at south without
stopping in between
Angle of declination: angle that a compass
needle deviates from the north geographic pole
 Angle of dip: the angle that the magnetic field
makes with respect to the surface at any point
 Magnetic north pole: true north pole as
generated by the earth due, most likely, to
currents of iron moving in the core
 Geographic north pole: where the Earth’s axis
of rotation crosses the surface in the Northern
Hemisphere
 Click here for an interactive description of the
difference.
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Magnetic force can be added to our bucket list of forces
that can cause objects to accelerate and can be used in
conjunction with Newton’s 2nd Law of Motion.
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For a Charge to Experience a magnetic force when place in a
field:
1. The charge must be moving, for no magnetic
force acts on a stationary charge.
2. The velocity of the moving charge must have a
component that is perpendicular to the direction
of the magnetic field.
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If the charge moves parallel or antiparallel to
the field, the charge experiences no magentic
force.
If the charge moves perpendicular to the
field, the charge experience the maximum
possible magnetic force.
If the charge moves at an angle, θ, only the
velocity component (vsinθ), perpendicular to
the field gives rise to a magnetic force.
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Extend the right hand so the fingers point
along the direction of the magnetic field (B)
and the thumb points along the velocity of
the charge. The palm of the hand, then,
faces in the direction of the magnetic force
that acts on a positive test charge.
If the moving charge is negative, the direction
of the magnetic force is opposite from
described above.
B
F
q 0 v sin 
• Direction of field is determined by a small compass needle.
• SI Unit: Newton second/coulomb meter = 1 Tesla
• If magnetic field is much less than one Tesla, a gauss (G) is
often used as a unit for magnetic field.
• 1 gauss = 10-4 tesla
ELECTRIC FIELD
MAGNETIC FIELD
Direction of electric force is
same as direction of
electric field
 Force does work and
increases KE
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Direction of magnetic force
is always perpendicular to
magnetic field and velocity
 Since displacement and
force are perpendicular, no
work is done by this force
 Force changes direction
but not magnitude of
velocity
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When a +q charge is moving perpendicular to a
magnetic field, the magnetic force causes the
particle to move in a circular path.
𝑚𝑣 2
 𝐹𝑐 =
𝑟
𝑚𝑣
 𝑟=
𝑞𝐵
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Radius of the circle is inversely proportional to
the magnitude of the magnetic field
Stronger fields produce “tighter” circular paths
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Since an electric current is a collection of moving
charges, a current in the presence of a magnetic
field can also experience a magnetic force
Modify RHR-1 by replacing direction of velocity
with direction of conventional current in order to
determine direction of force.
The magnetic force is maximum when the wire
is oriented perpendicular to the magnetic field.
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∆𝑞
𝑣∆𝑡𝐵𝑠𝑖𝑛𝜗
∆𝑡
𝐹=
Simplified, this equation becomes
 𝐹 = 𝐼𝐿𝐵𝑠𝑖𝑛𝜗
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The direction of the force of the magnetic
field is determined by using RHR-1 as
explained on previous slide.
If the direction of the current changes, the
direction of the force will also change.
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If a loop of wire is suspended properly in a
magnetic field, the magnetic force produces a
torque that can rotate the loop.
This torque is responsible for the operation of an
electric motor.
When a current-carrying loop is placed in a
magnetic field, the loop tends to rotate such
that its normal becomes aligned with the
magnetic field.
Basically, the current loop behaves like a magnet
suspended in a magnetic field.
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http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html#c1
http://www.learnapphysics.com/apphysicsb/magnetism.php
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A current-carrying wire will produce a
magnetic field of its own.
A compass needle will align itself with the net
magnetic field produced by a current and the
magnetic field of the earth
Thus, the beginning of the study of
electromagnetism.
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Compass needles indicate that the magnetic
field lines produced by the current are circles
centered on the wire.
If the current reverses, the needles reverse.
Direction of field found by RHR-2
RHR-2: curl the fingers of the right hand into the
shape of a half circle. Point the thumb in the
direction of the conventional current, I and the
tips of the fingers will point in the direction of
the magnetic field 𝐵.
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Magnitude of B is directly proportional to I
and inversely proportional to the radial
distance from the wire
𝜇0 𝐼
𝐵=
2𝜋𝑟
𝜇0 is known as the permeability of free space
with a value of 4π x 10-7 Tm/A