Download C_Magnetism_Notes 2009

Physics C
Magnetism
Name:_____________________
How are magnetic fields formed?
Sample Problem: Sketch the path and calculate the
acceleration. E=2000 N/C, and v = 2,000 m/s (figure on the
right)
What do magnetic fields exert a force upon?
Units of magnetic field:
Draw magnetic field lines:
Sample Problem: Sketch the path and calculate the acceleration.
B = 2.0 T, and v = 2,000 m/s (for figure on the right).
What can magnetic forces do to charged
particles?
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Equation for magnetic force on current-carrying
wire:
Derive this expression!
What can magnetic forces NOT do to charged
particles?
Sample Problem: A wire carries a current of
2.40 Amperes through a uniform magnetic field
B=1.6 k Tesla. What is the force on a 0.75 meter
long section of the wire if the current moves in
the +x direction?
Equation for Magnetic Force:
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x
Sample Problem
How much current must be flowing through a
horizontal 20.0 meter long wire to suspended in
a 5.0 T magnetic field if the wire has a mass of
0.20 kg?
Sample Problem: A charge of mass m and charge q moves at
speed v at right angles to magnetic field B as shown. Derive an
expression for the path of the particle as a function of charge,
mass, speed, and magnetic field strength.
V
+q
B
If the current is flowing north, in what direction
must be the magnetic field?
Magnetic Force

What can be concluded about the sign
of the charge of each particle?
Torque on Wire Loop
B
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Crossed electric and magnetic fields can be
“velocity filters”
B
Sample Problem: Calculate the torque on a 40.0
cm length of wire, bent into a square, if it carries
20.0 amperes of electrical current with its normal
perpendicular to a magnetic field of strength
0.520 T.
p+
v
E
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Write Ampere’s Law
Currents Cause Magnetic
Fields
i
B
Maxwell Equations:
Gauss’s Law of Electricity
r
Gauss’s Law of Magnetism
Ampere’s Law
Currents Cause Magnetic Fields

Try using the hand rule to tell you how the
magnetic field curls around these currents.
Faraday’s Law of Induction
•
Sample Problem: Use Ampere’s Law to derive
the magnetic field a distance r from the center of
a wire of radius R carrying current Io, where r >
R.
Sample Problem: Two parallel wires have
currents of I1 and I2 in exactly the same
direction. Define the magnitude and direction of
the force they exert on each other.
Sample Problem: Use Ampere’s Law to derive
the magnetic field a distance r from the center of
a wire of radius R carrying current Io, where
r<R.
Sample Problem: Two parallel wires have
currents of I1 and I2 in exactly the opposite
direction. Define the magnitude and direction of
the force they exert on each other.
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Define Displacement Current
Ampere’s Law
Write Ampere’s Law with Displacement
Current:
B
r
R
Magnetic Flux:
Io
R
Draw a loop with maximum flux
Sample problem: Using Ampere’s Law, show that the
magnetic field inside a solenoid has magnitude B = oIon
Draw a loop with minimum flux
Sample Problem: Use Ampere’s Law to derive the magnetic
field at various spots around the Toroid.
Draw a loop with intermediate flux
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Equation for magnetic flux:
Hall Effect Notes:
Sample Problem: Calculate the magnetic flux
through a rectangular wire frame 3.0 m long and
2.0 m wide if the magnetic field through the
frame is 4.2 mT.
a) Assume that the magnetic field is
perpendicular to the area vector.
b) Assume that the magnetic field is parallel to
the area vector.
c) Assume that the angle between the magnetic
field and the area vector is 30o.
•
Magnetic Dipole Moment Notes:
Sample Problem: Assume the angle is 40o, the magnetic field is 50 mT, and
the flux is 250 mWb. What is the radius of the loop?
B
A
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Write expressions for Faraday’s Law of
Induction:
Sample Problem: A 50 turn rectangular coil of
dimensions 5.0 cm x 10.0 cm is allowed to fall
from a position where B = 0 to a new position
where B = 0.500 T and is directed perpendicular
to the plane of the coil. Calculate the magnitude
of the average emf if this occurs in 0.250
seconds.
What is the unit of magnetic flux?
How do you induce an electric potential using
flux?
Sample Problem: A loop of area A is placed in
a region where the magnetic field is
perpendicular to the plane of the loop. The
magnitude of the field is allowed to vary in time
according to
State Lenz’s Law:
B  Bmax e
 1
What is the function defining the emf of the
loop? Obtain the value for the emf at t = 4.0
seconds.
Sample problem: What is the current produced in a loop of radius 16
cm and resistance 8.5  at different times shown below? Assume the
loop has an orientation in which it receives maximum magnetic flux.
1.0
B (T)
0.5
0
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t (s)
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• Sample Problem: The magnetic field is increasing at a rate of
4.0 mT/s. What is the direction of the current in the wire loop?
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Sample problem: How much current flows through the resistor?
How much power is dissipated by the resistor?
• Sample Problem: The magnetic field is increasing at a rate of
4.0 mT/s. What is the direction of the current in the wire loop?
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50
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B = 0.15
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• Sample Problem: The magnetic field is decreasing at a rate of
4.0 mT/s. The radius of the loop is 3.0 m, and the resistance is
4 . What is the magnitude and direction of the current?
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v = 2 m/s
Looking at Faraday’s Law a new way
• Sample problem: A circular magnetic field of radius 1.0 meter
is decreasing at a rate of 4.0 mT/s. What is the magnitude of
the induced electric field 0.50 m from the center of the magnetic
field during this time? What about at 1.0 m? at 1.2 m?
What do we mean by the term “motional emf”?
Give the equation for “motional emf”
Derive this expression!
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What is an inductor?
Draw a circuit with a cell and an inductor, and
indicate the direction of the current and the back
emf just after the switch is opened.
How do you draw an inductor in a circuit?
What is meant by the term inductance?
Derive an expression for the self-inductance of a
long solenoid
What are the units of inductance?
Define self-inductance:
Sample problem: A coil has an inductance of
3.00 mH and the current changes from 0.200 A
to 1.5 A in a time of 0.200 s. Find the magnitude
of the average induced emf in the coil during this
time.
Give an equation for the self-inductance of an
inductor in a circuit.
Draw a circuit with a cell and an inductor, and
indicate the direction of the current and the back
emf just after the switch is closed.
Definition of an RL Circuit:
What does the inductor do in an RL circuit?
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Draw an RL Circuit and indicate the direction of
the back emf just after the switch is closed.
Derive an expression for the voltage across the
inductor and the resistor as functions of time.
Draw graphs of the voltage and current in the
circuit when the switch is first closed:
Draw an RL Circuit and indicate the direction of
the back emf just after the switch is opened.
Derive an expression for the voltage across the
inductor and the resistor as functions of time.
Draw graphs of the voltage and current in the
circuit when the switch is first opened:
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What is meant by the inductive time constant?
How do you calculate the magnetic energy stored
in an inductor?
How do you calculate the inductive time
constant?
Sample problem: Calculate the energy
associated with the magnetic field of a 200 turn
solenoid in which a current of 1.75 A produces a
flux of 3.7 x 10-4 T m2.
Sample problem: A 12.0 volt battery is
connected in series with a 10.0  resistor and a
2.00 H inductor. How long will it take the
current to reach 50% of its final value?
Sample problem: An RL circuit in which L =
4.00 H and R = 5.00  is connected to a 22.0 V
battery at t=0. What energy is stored in the
inductor when the current is 0.50 A? At what
rate is energy being stored when the current is
1.00 A?
Sample problem: How much resistance is in an
RL circuit in which L = 2.50 H and the current
increases to 90% of its final value in 3.0 s?
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