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Faraday’s Law:

“The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.”

Lenz’s Law Why circuits obey Newton’s third law along with the

conservation of energy “An induced electromotive force (emf) always gives

rise to a current whose magnetic field opposes the original change in magnetic flux”

Called “Eddy” since they are analogous to fluid eddies in formation and behavior

Responsible for the opposing magnetic fields that produce drag and heating effects

The drag effects give rise to induction braking Absent external potentials will result in the system

coming to a halt Heating effects are exploited by devices such as

induction cookers If left unchecked, then it could result in serious

damage to mechanical/circuit components

High voltage circuits are constructed as a series of “laminations” to reduce eddy currents

Solid conductors would suffer increased resistivity and large energy losses (heat)

Not to be confused with stellar magnetic braking The primary reason for slow stellar rotations

Utilized in many practical applications: Trains (Maglev and conventional) as a braking system Some roller coasters Braking Industrial equipment and power tools Some exercise equipment

Rowing or Spin machines… to increase resistance Determining structural defects in conductive materials Metal Detectors

Metal disc, on the end of a rotor assembly, placed between two electromagnets

Static bank of magnets/conductors located on the tracks with conductors/magnets on the car

Quiet Almost no wear

Wear only if coolant system failure

Essentially zero maintenance

Produce no chemical pollution Dust Smell Physical waste No toxic chemicals

Need conventional brakes to hold a vehicle stationary

In reality certain sections of railroad tracks have lots of brake activity Excess heat would

cause structural issues Reduce brake

effectiveness Increased cost

Still not widely used Basic idea has been around since the

industrial revolution Flywheels (mechanical capacitor)

Flywheels still used, but eddy currents can be exploited for this end as well

Capture the energy from the induced currents instead of it just being allowed to dissipate as heat

Avoids problem of having to carry around big flywheels

Copper pipe & Neodymium magnets

Pipe Dimensions: ½” and ¾” diameter (outer)

pipes both ≈ 1/32” thick Magnets: (NdFeB)

½” diameter N42 Axially magnetized Pull Force: 3.1 lbs Surface Field: 1601 Gauss

(0.1601 T) Magnets have been

weakened due to an living an abused life

For increase braking effect: More powerful magnet Thicker contiguous pipe Use more strongly

conductive diamagnetic material

Lower temperature (pipe not magnet)

Believed to be caused by the alteration of the electron orbital velocities Alters magnetic dipole moment Field will oppose the the magnetic field changes due to the external field

Caused by quantum mech (Landau Levels) Copper – Diamagnetic Diamagnetism primarily responsible for the Lenz Law interaction Superconductors completely repel external magnetic fields

All conductors exhibit an effective diamagnetism when they experience a changing magnetic field. The Lorentz force on electrons causes them to circulate around forming eddy currents. The eddy currents then produce an induced magnetic field which opposes the applied field, resisting the conductor's motion.

Joke: Of course if I could have had some gold piping the effect could have been much stronger but I probably wouldn’t have brought it to class

Magnetic permeability < or = 1 All conductors exhibit an effective diamagnetism when they experience a

changing magnetic field. The Lorentz force on electrons causes them to circulate around forming eddy currents. The eddy currents then produce an induced magnetic field which opposes the applied field, resisting the conductor's motion.

Pic: Neodynium iron boron mags What does 42 MGOe mean?

Mega Gauss Oersted – magnetic energy product