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Ph126 Spring 2008Lecture #8
Magnetic Fields Produced by
Moving Charges Prof. Gregory Tarlé[email protected]
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Last Lecture: Magnetic Forces Moving charges can
experience forces in magnetic fields: Magnitude:
Direction: Right-Hand Rule
Magnetic force does no work on the moving charge
Measure magnetic field in Tesla (T)
sinvBqF
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Electric vs. Magnetic Forces The electric force is always in the direction of the
electric field, but the magnetic force is always perpendicular to the magnetic field
The electric force acts on a charged particle independent of the particle’s velocity, but the magnetic force acts on a charged particle only when it is in motion
The electric force can change the speed of a charged particle while the magnetic force associated with a steady magnetic field changes the direction of the particle, but not its speed
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Concept Test #1What direction is the force this wire feels because of the magnetic field?
1) To the right
2) To the left
3) Up the page
4) Down the page
5) Into the page
6) Out of the pageCurrent I
Magnetic Field B
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Magnetic Force on a Current
sinqvBF
sinB
L
tv
I
t
qF
sinILBF angle between I and B
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Torque on a Current-Carrying Coil
The two forces on the loop have equal magnitude but they are opposite in direction.
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Concept Test #2A square loop carries a current I and pivots without friction about the z-axis. A uniform magnetic field B points in the +x direction, and the loop initially makes an angle θ with the x-z plane. The torque on the loop is clockwise.
True (yes) False (no)
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Calculate the Torque
sinsin
sin
21
21
IABwILB
wILB
sin
momentmagnetic
BNIA N = number of turns of wire
"" ckwisecounterclo
""clockwise :Direction
sin :Recall Fr
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Max and Min Torques
The loop tends to rotate such that its normal becomes aligned with the magnetic field
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Origins of Magnetic Fields Magnetic fields come from:
• Magnets• Moving charges (i.e. currents)• Changing E fields (more next lecture…)
Magnetic field lines never end; they must form closed loops
No magnetic charges (monopoles) exist
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B produced by a long straight wire
r
IB o
2
AmT104 7 o
permeability of free space
Increases with current, falls off with distance
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Direction of B field of a straight wire The magnetic field
due to the current in a long straight wire has circular field lines around the wire
The direction of the
field is given by the right hand rule
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Concept Test #3Two identical parallel long straight wires carrying a current I stand a distance r apart. Which of the following statements is false?
1) The magnetic field B created by the bottom wire at P points out of the page.
2) The force exerted by the bottom wire on the top wire is F = ILB.
3) The force pushes the top wire up.
F
P
I
I
L
r
r
IB oP
2
r
IL
r
IILF oo
22
2
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Concept Test #4Two parallel long straight wires carrying currents I and 2I stand a distance r apart. Which of the following statements is false?
1) The magnetic force pulls the top wire down toward the bottom wire.
2) The magnetic force pulls the bottom wire up toward the top wire.
3) The magnetic force on the top wire is greater than the magnetic force on the bottom wire.
P
I
2I
L
F r
the two wires generate magnetic fields that pull one another toward each other Newton’s 3rd Law.
r
ILF o
2
2 2
21
The force is attractive if the currents are in the same direction and repulsive otherwise
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Electromagnet Current flowing in a loop of wire creates a
magnetic field Current loop can be imagined to be a phantom bar
magnet
=
http://www.windows.ucar.edu/spaceweather/info_mag_fields.html
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Right hand rule
Which side is north pole?
N
S
At center of circular loop
R
INB o
2
number of turns
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B produced by a solenoid
Interior of a solenoid
nIB onumber of turns per unit length
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Ampere’s Law Ampere’s law relates sum of
B field along a line to current inside
Formally:
IB o ||
net current passing through surface bounded by path
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B field of wire from Ampere’s Law
IB o
IrB o 2
IB o ||
r
IB o
2
Same as before!
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=
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N
S