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
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
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