The Large Hadron Collider at CERN

~1200 dipole magnets

My house

The LHC dipole magnets With an ingenious design intense electric currents two electric fields are produced in opposite directions to keep protons in orbit

The larger R, the greater v (and energy) LHC: R=4.4 Km

Is the LHC Dangerous?

No, it’s not

We are bombarded every day with energetic cosmic rays and I am still playing!

Energy Spectrum of Cosmic Rays

Earth is bombarded everyday with cosmic particles with huge energy, much larger than the proton collisions at the LHC

LHC

CERN: the birth place of the internet

Physics 202, Lecture 15 Today’s Topics

  Faraday’s Law (Ch 31)

  Change of Magnetic Flux and Emf (ε)   Lenz’s Law   Faraday’s Law of Induction

Electromotive Force (emf, ε)   Electromotive “force”, emf, is a measure of the voltage

that can be provided by a source.   For a given device, if a charge Q passes through that

device, and gains an energy U, the net emf for that device is the energy gained per unit charge, or U/Q.

  emf is not a force, it has a unit of volts   sources of emf: •  chemical process (battery) •  change of magnetic flux •  semiconductors…..

 e.g. battery:   notice that emf has a direction   emf may exist even if no current.

+

-

1.5V

+ -

-------

+++++

ε= 1.5V

Demo: Emf and Change of Magnetic Flux

Lenz’s Law  The emf due to change of magnetic flux tends to

create a current which produces a magnetic field to compensate the change of original magnetic flux.   Lenz’s law is a convenient way to determine the

direction of the emf due to magnetic flux change.

Demo: Eddy Current

Formulation of Faraday’s Law  The emf induced in a “circuit” is proportional to the

time rate of change of magnetic flux through the “circuit”.

  Notes:   “Circuit”: any closed path

 does not have to be real conducting circuit

  The path/circuit does not have to be circular, or even planar

dtd BΦ−=ε

A

B

θ

∫ •=Φ AB dB

nominal direction of ε

Direction of Induced emf

  ε>0, same as nominal direction

ε<0, opposite

  Note that the nominal direction of ε and the direction of vector A follows right hand rule

dtd BΦ−=ε

A

B

θ

∫ •=Φ AB dB

nominal direction of ε

Methods to Change Electric Flux

 Change of ΦB emf   To change ΦB:

  Change B emf produced by an induced E field   Change A motional emf   Change ϑ motional emf   Combination of above

dtBAd

dtd

uniform

)cos( θε −Φ

−= =B

B