Transcript PHY2054_02-22

Announcements
• WebAssign HW Set 6 due this Friday
• Problems cover material from Chapters 19
• Prof. Kumar tea and cookies today from 5 – 6
pm in room 2165
• mine are 2 - 3 pm Thursday, room 2265
• also, can schedule by appointment
• Exam 1 statistics
QUESTIONS? PLEASE ASK!
•Average: 14.43
• Standard deviation: 3.44
From last time
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Magnets and earth’s magnetic
field
F
Magnetic Fields: B º
qvsin q
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Units are T = N/A.m
Use right hand rule to determine
direction of force
Force on a wire:
F = B I L sin θ
Torque on a Current Loop
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Torque t = B I A N sin q
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Applies to any shape loop
N is the number of turns in the
coil
Torque has a maximum value
of NBIA (when q = 90°)
Torque is zero when the field is
parallel to the plane of the loop
Magnetic Moment m = IAN
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m is a vector
Torque can be written as
t = mB sinq
m
Example Problem 19.31
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A long piece of wire with a mass of
0.100 kg and a length of 4.00 m is
used to make a square coil with a
side of 0.100 m. The coil is hinged
along a horizontal side, carrying a
3.40 A current, and is placed in a
vertical magnetic field of 0.010 T.
(a) Determine the angle that plane
of the coil makes with the vertical
when the coil is in equilibrium. (b)
Find the torque acting on the coil
due to the magnetic force at
equilibrium
Electric Motor
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electric motor - converts
electrical energy to
mechanical energy
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The mechanical energy is
in the form of rotational
kinetic energy
An electric motor
consists of a rigid
current-carrying loop
that rotates when
placed in a magnetic
field
Electric Motor
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Torque acting on the
loop will rotate the loop
to smaller values of θ
until the torque
becomes 0 at θ = 0°
If the loop turns past
this point and the
current remains in the
same direction, the
torque reverses and
turns the loop in the
opposite direction
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Bad!!
Electric Motor
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So, we need to be
clever…
To provide continuous
rotation in one direction,
the current in the loop
must periodically
reverse
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In AC motors, this
reversal naturally occurs
In DC motors, a split-ring
commutator and brushes
are used
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Actual motors would
contain many current
loops and commutators
Force on a Charged
Particle in a Magnetic Field
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Consider a particle
moving in an external
magnetic field so that its
velocity is perpendicular
to the field
The force is always
directed toward the
center of the circular path
The magnetic force
causes a centripetal
acceleration, changing
the direction of the
velocity of the particle
Force on a Charged Particle
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Equating the magnetic and centripetal
forces:
2
mv
F = qvB =
r
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mv
Solving for r: r =
qB
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r is proportional to the momentum of the
particle and inversely proportional to the
magnetic field
Sometimes called the cyclotron equation
Particle Moving in an External
Magnetic Field
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If the particle’s
velocity is not
perpendicular to the
field, the path
followed by the
particle is a spiral
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The spiral path is
called a helix
Example Problem 19.42
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A cosmic ray proton in interstellar space
has an energy of 10 MeV and executes a
circular orbit having a radius equal to that
of Mercury’s orbit around the Sun (5.8 x
1010 m). What is the magnetic field in
that region of space?
Solution to 19.31
Solution to 19.42