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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