Slide 1
Magnetism
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Chapter 27 opener. Magnets produce magnetic fields, but so do electric cu
ents. An electric cu
ent flowing in this straight wire produces a magnetic field which causes the tiny pieces of iron (iron “filings”) to align in the field. We shall see in this Chapter how magnetic field is defined, and that the magnetic field direction is along the iron filings. The magnetic field lines due to the electric cu
ent in this long wire are in the shape of circles around the wire. We also discuss how magnetic fields exert forces on electric cu
ents and on charged particles, as well as useful applications of the interaction between magnetic fields and electric cu
ents and moving electric charges.
Magnets and Magnetic Fields
Electric Cu
ents Produce Magnetic Fields
Force on an Electric Cu
ent in a Magnetic Field; Definition of B
Force on an Electric Charge Moving in a Magnetic Field
Torque on a Cu
ent Loop; Magnetic Dipole Moment
Units
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Applications: Motors, Loudspeakers, Galvanometers
Discovery and Properties of the Electron
The Hall Effect
Mass Spectromete
Units
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Magnets have two ends – poles – called north and south.
Like poles repel; unlike poles attract.
Magnets and Magnetic Fields
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Figure 27-2. Like poles of a magnet repel; unlike poles attract. Red a
ows indicate force direction.
However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.
Magnets and Magnetic Fields
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Figure 27-3. If you split a magnet, you won’t get isolated north and south poles; instead, two new magnets are produced, each with a north and a south pole.
Magnetic fields can be visualized using magnetic field lines, which are always closed loops.
Magnets and Magnetic Fields
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Figure XXXXXXXXXXa) Visualizing magnetic field lines around a bar magnet, using iron filings and compass needles. The red end of the bar magnet is its north pole. The N pole of a nea
y compass needle points away from the north pole of the magnet. (b) Magnetic field lines for a bar magnet.
The Earth’s magnetic field is similar to that of a bar magnet.
Note that the Earth’s “North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it.
Magnets and Magnetic Fields
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Figure 27-5. The Earth acts like a huge magnet; but its magnetic poles are not at the geographic poles, which are on the Earth’s rotation axis.
A uniform magnetic field is constant in magnitude and direction.
The field between these two wide poles is nearly uniform.
Magnets and Magnetic Fields
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Figure 27-7. Magnetic field between two wide poles of a magnet is nearly uniform, except near the edges.
Experiment shows that an electric cu
ent produces a magnetic field. The direction of the field is given by a right-hand rule.
Electric Cu
ents Produce Magnetic Fields
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Figure XXXXXXXXXXa) Deflection of compass needles near a cu
ent-ca
ying wire, showing the presence and direction of the magnetic field. (b) Magnetic field lines around an electric cu
ent in a straight wire. (c) Right-hand rule for remembering the direction of the magnetic field: when the thumb points in the direction of the conventional cu
ent, the fingers wrapped around the wire point in the direction of the magnetic field. See also the Chapter-Opening photo.
Electric Cu
ents Produce Magnetic Fields
Here we see the field due to a cu
ent loop; the direction is again given by a right-hand rule.
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Figure 27-9. Magnetic field lines due to a circular loop of wire.
Figure XXXXXXXXXXRight-hand rule for determining the direction of the magnetic field relative to the cu
ent.
A magnet exerts a force on a cu
ent-ca
ying wire. The direction of the force is given by a right-hand rule.
Force on an Electric Cu
ent in a Magnetic Field; Definition of B
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Figure XXXXXXXXXXa) Force on a cu
ent-ca
ying wire placed in a magnetic field B; (b) same, but cu
ent reversed; (c) right-hand rule for setup in (b).
The force on the wire depends on the cu
ent, the length of the wire, the magnetic field, and its orientation:
This equation defines the magnetic field B.
In vector notation:
27-3 Force on an Electric Cu
ent in a Magnetic Field; Definition of B
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Unit of B: the tesla, T:
1 T = 1 N/A·m.
Another unit sometimes used: the gauss (G):
1 G = 10-4 T.
27-3 Force on an Electric Cu
ent in a Magnetic Field; Definition of B
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27-3 Force on an Electric Cu
ent in a Magnetic Field; Definition of B
Example 27-1: Magnetic Force on a cu
ent-ca
ying wire.
A wire ca
ying a 30-A
cu
ent has a length l = 12
cm between the pole
faces of a magnet at an
angle θ = 60°, as shown.
The magnetic field is
approximately uniform at
0.90 T. We ignore the field
eyond the pole pieces.
What is the magnitude of
the force on the wire?
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Solution: F = IlBsin θ = 2.8 N.
27-3 Force on an Electric Cu
ent in a Magnetic Field; Definition of B
Example 27-2: Measuring a magnetic field.
A rectangular loop of wire hangs vertically as shown. A magnetic field B is directed horizontally, perpendicular to the wire, and points out of the page at all points. The magnetic field is very nearly uniform along the horizontal portion of wire ab (length l = 10.0 cm) which is near the center of the gap of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward magnetic force (in addition to the gravitational force) of F = 3.48 x 10-2 N when the wire ca
ies a cu
ent I = 0.245 A. What is the magnitude of the magnetic field B?
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Solution: The wire is perpendicular to the field (the vertical wires feel no force), so B = F/Il = 1.42 T.
The force on a moving charge is related to the force on a cu
ent:
Once again, the direction is given by a right-hand rule.
27-4 Force on an Electric Charge Moving in a Magnetic Field
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Figure XXXXXXXXXXForce on charged particles due to a magnetic field is perpendicular to the magnetic field direction.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Conceptual Example 27-4: Negative charge near a magnet.
A negative charge -Q is placed at rest near a magnet. Will the charge begin to move? Will it feel a force? What if the charge were positive, +Q?
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Solution: There is no force on a motionless charge, be it positive or negative, so in neither case will it begin to move.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Example 27-5: Magnetic force on a proton.
A magnetic field exerts a force of 8.0 x 10-14 N toward the west on a proton moving vertically upward at a speed of 5.0 x 106 m/s (a). When moving horizontally in a northerly direction, the force on the proton is zero (b). Determine the magnitude and direction of the magnetic field in this region. (The charge on a proton is q = +e = 1.6 x 10-19 C.)
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Solution: Since the force is zero when the proton is moving north, the field must point in the north-south direction. In order for the force to be to the west when the proton is moving up, the field must point north. B = F/qv = 0.10 T.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Example 27-6: Magnetic force on ions during a nerve pulse.
Estimate the magnetic force due to the Earth’s magnetic field on ions crossing a cell mem
ane during an action potential. Assume the speed of the ions is 10-2 m/s.
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Solution: F = qvB; assume B = 10-4 T, and use the electron charge for q. F = 10-25 N.
If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle.
27-4 Force on an Electric Charge Moving in a Magnetic Field
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Figure XXXXXXXXXXForce exerted by a uniform magnetic field on a moving charged particle (in this case, an electron) produces a circular path.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Example 27-7: Electron’s path in a uniform magnetic field.
An electron travels at 2.0 x 107 m/s in a plane perpendicular to a uniform 0.010-T magnetic field. Describe its path quantitatively.
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Solution: The magnetic force keeps the particle moving in a circle, so mv2
= qvB. Solving for r gives r = mv/qB = 1.1 cm.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Conceptual Example 27-8: Stopping charged particles.
Can a magnetic field be used to stop a single charged particle, as an electric field can?
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Solution: No, because the force is always perpendicular to the velocity. In fact, a uniform magnetic field cannot change the speed of a charged particle, only its direction.
Problem solving: Magnetic fields – things to remember:
The magnetic force is perpendicular to the magnetic field direction.
The right-hand rule is useful for determining directions.
Equations in this chapter give magnitudes only. The right-hand rule gives the direction.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge Moving in a Magnetic Field
Conceptual Example 27-9: A helical path.
What is the path of a charged particle in a uniform magnetic field if its velocity is not perpendicular to the magnetic field?
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Solution: The path is a helix – the component of velocity parallel to the magnetic field does not change, and the velocity in the