v b ee ???? + - v>0 hall effect h. v b ee >0 + - v>0 v b ee ???? + - v
TRANSCRIPT
v
B
E
>0
+-
V>0
v
B
E
????
+-
V<0
Hall Effect for Opposite Charges
Current: many charges are movingSuperposition: add up forces on individual charges
Number of moving charges in short wire:
Total force: I
Force of a short wire:
In metals: charges q are negative. Will this equation still work?
Magnetic Force on a Current-carrying Wire
What is the total force on this wire?
What is the magnitude of the forceon part L if: I = 10 AB = 1 TL = 10 cm
Exercise
IB
F
What will happen if currentis reversed?
What will happen if magnetis reversed?
Experiment
Ampere is defined as a current at which two very long parallel wires 1 m apart create a force on each other of 2.10-7 N per meter length.
From this also follows that 0/(4) = 10-7 T.m/A
Forces Between Parallel Wires
Definition of 1 Ampere:
For long wire:
Magnetic force on lower wire: Magnetic force on upper wire:
What if current runs in opposite directions?
Forces Between Parallel Wires
Electric forces: “likes repel, unlikes attract”Magnetic forces: “likes attract, unlikes repel”
Magnetic force acts only on moving charges
Mobile electrons experience magnetic force
The motion of the wire is an electric side-effect of the magnetic force on the moving electrons.
Why does the Wire Move?
Atomic cores are not moving – no magnetic force!Atomic cores feel an unbalanced force. Wire movesdown!
Metal bar
Fm
polarization
Static equilibrium:
Metal is in static equilibrium: but E 0 inside!
What is V ?
Currents Due to Magnetic Forces
Metal bar
Fm
Static equilibrium:
How much force do weneed to apply to keepthe bar moving at constantspeed?
Does this polarized bar remind you anything we’ve already studied?
Currents Due to Magnetic Forces
Fm
Non-Coulomb forcedrives e against FE
Non-Coulomb work:
What is emf of this ‘battery’?
Non-Coulomb work per unit charge:
Bar may have some resistance rint:
‘motional emf’
Non-Coulomb Work
What electric fields are produced by the surface charges?
Is round trip V zero?
Round-trip Potential
Round trip due to these Coulomb electric fields has to be zero.
E
E
P=IV=I(emf) Are we getting something for nothing?
Fm
Bar – current I:
FI F
Work:
Power:
Main principle of electric generators:Mechanical power is converted to electric power
Moving Bar and Energy Conservation
x
A current carrying loop has a tendency to twist in magnetic field
Compass needle: collection of atomic current loops
Magnetic Torque on a Magnetic Dipole Moment
Torque () = distance from the axle (lever arm) times perpendicular component of the force.
Works with loops of any shape!
Magnetic Torque: Quantitative Analysis
Calculate amount of work needed to rotate from angle I to f:
Potential energy for a magnetic dipole moment
Magnetic Dipole Moment: Potential Energy
Potential energy for a magnetic dipole moment
U= min-µB
0 maxµB
0
What is the energy difference between the highest and the lowest state?
Picture of the U and µ in magnetic field – important in atomic and nuclear physics.
Magnetic Dipole Moment: Potential Energy
charged tape
Any magnetic field?
Reference Frame
Two protons
+e
+e
r
1
2
v
v
Electric force:
E1
F21,e
Magnetic field:
B1 Magnetic force:
F21,m
Magnetic Forces in Moving Reference Frames
Electric force:
Magnetic force:
+e
+e
r
1
2
v
v
E1
F21,e
B1
F21,m
Ratio:
(m/s)2
=c2
it is not accidental!
Magnetic Forces in Moving Reference Frames
+e
+e
r
1
2
v
v
E1
F21,e
B1
F21,mFor v<<c the magnetic force is muchsmaller than electric force
How can we detect the magnetic force ona current carrying wire?
Full Lorentz force:
Magnetic Forces in Moving Reference Frames
downward
+e
+e
r
1
2
v
v
E1
F21,e
B1
F21,mWho will see protons hitfloor and ceiling first?
20 ns
15 ns
Time must run slower in moving frame.
Einstein 1905: “On the electrodynamics of moving bodies”
Magnetic Forces in Moving Reference Frames
v
E
Moving Through a Uniform Magnetic Field
There may be different mechanisms for different observers in different reference frames, but all observers can correctly predict what will happen in their own frames, using the same relativistically correct physical laws.
The Principle of Relativity