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Chapter 22: Magnetism
Brent Royuk Phys-112
Concordia University
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Magnets • Magnets are caused by moving charges.
– Permanent Magnets vs. Electromagnets • Magnets always have two poles, north
and south. • Like poles repel, opposites attract.
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Magnets • North means north-seeking, so Earth’s
north pole is what kind of pole? • But any pole attracts metal: Why? • Bar magnets are dipoles. Can there be
a monopole? • History: lodestones and magnetic
compasses. Remember Magnesia? • Permanent magnets vs. electromagnets:
More later
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Magnetic Fields • The magnetic field
B surrounds magnets analogously to the electric field
• Is there an analog to Coulomb’s Law? No, the B-field is more complicated.
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B-Field Lines • Field line mapping: What defines a
field line? • The direction of the line is always
from N to S.
S N
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Earth’s Magnetic Field • Probably caused by currents in
Earth’s molten core • Drift and reversals
– Last reversal: 780,000 years ago
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What’s Wrong With This Picture?
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Magnetic Force on a Moving Charge • A moving charge moving in a
perpendicular direction through a B-field experiences a force perpendicular to its motion
• Qualitative: F ∝ qvB sin θ
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Electric Field Units • [B] = [F/qv] • 1 N/Am ≡ 1 tesla (T)
– Neutron star: 108 – Big magnet: 1.5 – Small bar magnet: .01 T – Interstellar space: 10-10 – Magnetically shielded laboratory:
10-13 • Another unit: 1 T = 104 gauss (G)
– Earth’s magnetic field: 0.5 G
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Magnetic Force on a Moving Charge • F = qvB sin θ
– Note that the force is maximum when perpendicular, minimum at parallel. Weird.
• What is the significance of a field line for a moving charge?
• Example: An electron moves at right angles to a magnetic field of 0.12 T. What is its speed if the force exerted on it is 8.9 x 10-15 N?
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Direction of the Magnetic Force • F = q(v x B)
– Math note: The parentheses are unnecessary • The Right Hand Rule
– Wrap or Point methods – In/Out conventions – Positive vs. Negative particles
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What’s Wrong With This Picture?
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Examples • What direction is the force acting on a charged particle
traveling west through Earth’s magnetic field? Down? South?
• A charge of +2.5 µC moves at 55 m/s left-to-right across the blackboard through a region with a field of 0.022 T that is out of the board. What force acts on it? What if the particle is charged negatively?
• An electron moving with a speed of 9.1 x 105 m/s in the positive x direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of 2.0 x 10-13 N that points in the negative z direction. What is the direction and magnitude of the magnetic field?
• Magnets and big old CRT screens.
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Motion of Charged Particles in B-Fields • How will a charged particle move
through a B-field? – Find the radius.
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Motion of Charged Particles in B-Fields • Helical motion of charged particles
from the sun (the solar wind).
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Velocity Selector • Traveling through crossed electric and
magnetic field, a charged particle feels two forces: qvB and qE.
• If the forces are equal, E = vB and there’s no net force.
• v = E/B
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Mass Spectrometer • The radius of the
trajectory measures the mass.
• But you must also know the charge. – Singly, doubly
ionized?
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Force on a Wire • Start with:
F = qvB sin θ q = It = IL/v, so
• F = ILB sin θ – Vector equivalent:
F = I(L x B)
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Force on a Wire • A Linear Motor • Which way would the bar move?
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Force on a Wire • In the picture below, the wire is
deflected downward. Which side of the magnet is a north pole?
• The monstrosity
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The Levitating Wire • A copper rod 0.150 m long and with a mass of
0.0500 kg is suspended from two thin flexible wires as shown below. At right angles to the rod is a uniform magnetic field of 0.550 T pointing into the picture. Find a) the direction and b) the magnitude of the electric current needed to levitate the copper rod.
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Application: Loudspeakers • A modulated current is sent to a voice
coil, which experiences a force from a magnet that is transmitted onto a speaker cone.
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Current Loops • A Rectangular Loop
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Current Loops • Generally, any
current-carrying loop in a magnetic field experiences a torque equal to: τ = NIAB sin θ
• This law also follows a right-hand rule...
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Current Loop Example • Use τ = NIAB sin θ to find the torque
on the loop below if I = 0.22 A and B = 0.050 T.
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Application: The Galvanometer • Torque on a coil of current loops is
balanced by a spring. • Galvanometers can be configured
as voltmeters or ammeters.
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Electromagnets • The Long, Straight Wire
– How long is it?
€
B =µ oI2πr
The Permeability of Free Space:
µo = 4π x 10-7 Tm/A
Another Right-Hand Rule:
Demo
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Long Straight Wire • What direction is the B-field a)
above both wires, b) below both wires, and c) between the wires?
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Solenoids • What is the direction of
the B-field in the vicinity of a current-carrying loop?
• The field at the center of a solenoid:
• Demo • Do two parallel current-
carrying wires attract or repel each other?
€
B =µoIN
L= µonI; n ≡
NL
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Magnetic Materials • Permanent magnets can create magnet fields
with “spinning” electrons. • In ferromagnetic materials like Fe and Ni this
tendency is strong. • Materials lose their magnetism above the Curie
Temperature (770 oC for Fe). – Ferromagnetic cores magnify the field in a solenoid.
• Diamagnetic materials become magnetic in response to B-fields.
• Paramagnetic materials do as well, but their B-field opposes the applied field. All materials display some paramagnetism.
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Ferromagnetic Materials • Domain Formation • Creating and destroying temporary
ferromagnets
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Electromagnet Summary