Download lecture 21 magnetic force

LECTURE 21
MAGNETIC FORCE
Instructor: Kazumi Tolich
Lecture 21
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Reading chapter 22.1 to 22.4
¤ Magnetic
fields
¤ Magnetic force on moving charges
¤ Motion of charged particles in a magnetic field
¤ Magnetic force on a current carrying wire
Magnets/Demo: 1
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North and south poles always come in pairs. Isolated magnetic
monopoles have not been experimentally observed.
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On Valentine’s day, 1982, there was one candidate monopole
observed, but this has never been reproduced and is likely caused by
stress relief in the detector.
Like magnetic poles repel each other, and opposite magnetic
poles attract each other.
Earth’s North Pole is a magnetic south pole because it attracts the
north pole of a compass needle.
Phys. Rev. Lett. 48 1378
Magnetic field and field lines
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Magnetic field is produced by moving charges and transmits the magnetic force.
Magnetic fields are visualized by magnetic field lines.
By definition, magnetic field lines exit from the north pole of a magnet and enter at
the south pole.
The density of field lines indicate the magnitude of the field.
Quiz: 1
5
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The figure shows several field line
patterns. Which of these field line
patterns can represent a magnetic
field? Check all that apply.
A.
B.
C.
D.
(a)
(b)
(c)
(d)
Quiz: 21-1 answer
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(b) and (d)
Magnetic field lines always make complete
loops. They neither begin nor end. So, (a) is
wrong.
If magnetic monopole existed, the field line
around it would look like that. But as far as
we know, magnetic monopoles do not exist.
Field lines never cross. So (c) is wrong.
Force by a magnetic field
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The magnitude and vector form of magnetic force on a moving charged
particle is given by
𝐹 = 𝑞 𝑣𝐵 sin 𝜃
𝐅⃗ = 𝑞𝐯 × 𝐁
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The right hand rule gives the direction of magnetic force on a positive
charge; the force on a negative charge would be in the opposite direction.
Quiz: 2
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A point charge moves a distance of 2.0 m in a magnetic field. During
this motion, the magnetic field exerts a force of constant magnitude of
1.0 N on the point charge. How much work is done by the magnetic
field on the charge in Joules?
Quiz: 21-2 answer
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0J
The direction of the magnetic force is
always perpendicular to the velocity.
¨ Non-zero work is done only if a force
is exerted in the direction of
displacement.
¨ Magnetic forces on point charges do
no work.
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Example: 1
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An alpha particle (charge 𝑞 = 3.2 × 10-19 C
and mass 𝑚 = 6.6 × 10-27 kg) travels at a
velocity, 𝑣, of magnitude 550 m/s through a
uniform magnetic field, 𝐵, of magnitude
0.045 T. The angle between 𝐯 and 𝐁 is
𝜃 = 52°. What are the magnitudes of
a)
the force acting on the particle due to the
magnetic field?
b)
the acceleration of the particle due to the
force?
c)
Does the speed of the particle change?
Quiz: 3
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Electrons travel at an initial velocity v0. They pass through a set of deflection
plates, between which there exists an electric field which deflects them
upwards toward point b. In which direction should a magnetic field be
applied so that the electrons land undeflected at a?
A.
B.
C.
D.
E.
F.
To the right
To the left
Up
Down
Into the page
Out of the page
b
a
Quiz: 21-3 answer/Demo: 2
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Into the page
For the electron to be undeflected, there must be a magnetic
force on the electron downward.
𝐅⃗ = 𝑞𝐯 × 𝐁 = −𝑒𝐯 × 𝐁
J. J. Thomson discovered electrons and measured the 𝑞⁄𝑚
ratio of electrons by shooting electrons in E and B fields.
¤ By tuning on the B field, velocity of electrons were
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measured: 𝑣 = .
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With the B field off, the amount of deflection depends
84
on 𝑎7 = .
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Demo: electron beam in magnetic field
eE
eevB
Circular motion in magnetic fields/Demo: 3
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If the magnetic field, 𝐵, is perpendicular to the
velocity of a particle with a mass 𝑚 and a charge
𝑞, moving at a speed 𝑣, then the particle undergoes
a uniform circular motion with a radius given by
𝑚𝑣
𝑟=
𝑞𝐵
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The mass spectrometer measures masses of isotopes.
Demo: fine beam tube
Helical motion
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If 𝐁 is not perpendicular to 𝐯, 𝐯;<=<>>?> does not change
since there is no magnetic force along that direction.
The particle moves in a helical path.
The helical path of an electron in a cloud chamber (a vessel
with a superheated vapor of water or alcohol).
What causes aurora?
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Charged particles ejected from the Sun (yellow and orange lines) are deflected by the Earths
magnetic field (red lines) entering the Earths atmosphere at the north and south magnetic poles.
The charged particles interact with the gas in the area to produce light.
Magnetic force on a current/Demo: 4
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For a current carrying wire, an external magnetic field exerts magnetic force on each of the
moving charges.
For a straight wire segment carrying a current I, the magnitude of the magnetic force is
𝐹 = 𝐼𝐿𝐵 sin 𝜃
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The direction of the magnetic force is given by the right hand rule.
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Demo: Jumping wire
Quiz: 4
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A horizontal wire carries a current flowing to the right and is in a vertical
magnetic field pointing up. What is the direction of the magnetic force on
the wire?
A.
B.
C.
D.
E.
F.
G.
Right
Left
Into the page
Out of the page
Up
Down
None of the above
I
B
Quiz: 21-4 answer
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Out of the page
Using the right-hand rule, we see that the magnetic force must point out of
the page.
Since F must be perpendicular to both I and B, F cannot be in the plane of
the page at all.
I
B
Quiz: 5
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A vertical wire carries a current upward and is in a vertical magnetic
field pointing up. What is the direction of the force on the wire?
A.
B.
C.
D.
E.
F.
G.
Right
Left
Into the page
Out of the page
Up
Down
None of the above
I
B
Quiz: 21-5 answer
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None of the above
¨ The magnitude of magnetic force on a current carrying wire is
given by 𝐹 = 𝐼𝐿𝐵 sin 𝜃, where 𝜃 is the angle between the
magnetic field and the direction of the current.
¨ So, 𝜃 = 0, and 𝐹 = 0.
¨ The direction of zero vector is undefined.
I
B
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Example: 2
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A straight, horizontal wire has a
current I = 28 A through it. Its
linear density is 46.6 g/m. What
are the magnitude and direction
of the minimum magnetic field B
needed to suspend the wire?
Example: 3
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A high-voltage power line carries a current of
I = 110 A at a location where the earth’s
magnetic field has a magnitude of
B = 0.59 G and points to the north, ϕ = 72°
below the horizontal. Find the direction and
magnitude of the magnetic force exerted on a
wire of a length L = 250 m if the current in
the wire flows
a)
b)
Horizontally toward the east or
Horizontally toward the south.