v B EE ???? + -  V>0 Hall Effect h

v B EE >0 + -  V>0 v B EE ???? + -  V<0 Hall Effect for Opposite Charges

Current: many charges are moving Superposition: 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 force on part L if: I = 10 A B = 1 T L = 10 cm Exercise

I B F What will happen if current is reversed? What will happen if magnet is 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 N per meter length. From this also follows that  0 /(4  ) = 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 moves down!

Metal bar FmFm polarization Static equilibrium: Metal is in static equilibrium: but E  0 inside! What is  V ? Currents Due to Magnetic Forces

Metal bar FmFm Static equilibrium: How much force do we need to apply to keep the bar moving at constant speed? Does this polarized bar remind you anything we’ve already studied? Currents Due to Magnetic Forces

FmFm Non-Coulomb force drives e against F E Non-Coulomb work: What is emf of this ‘battery’? Non-Coulomb work per unit charge: Bar may have some resistance r int : ‘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=I  V=I(emf) Are we getting something for nothing? FmFm Bar – current I: FIFI 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 0max µB 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 r 1 2 v v Electric force: E1E1 F 21,e Magnetic field: B1B1 Magnetic force: F 21,m Magnetic Forces in Moving Reference Frames

Electric force: Magnetic force: +e r 1 2 v v E1E1 F 21,e B1B1 F 21,m Ratio: (m/s) 2 =c 2 it is not accidental! Magnetic Forces in Moving Reference Frames

+e r 1 2 v v E1E1 F 21,e B1B1 F 21,m For v<<c the magnetic force is much smaller than electric force How can we detect the magnetic force on a current carrying wire? Full Lorentz force: Magnetic Forces in Moving Reference Frames downward

+e r 1 2 v v E1E1 F 21,e B1B1 F 21,m Who will see protons hit floor 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