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Review. Physics 122. Final Exam. Saturday, December 17, 8:30 am (sorry!) - Hoygt Final exam is based on the entire course PHY122. Last homework will be based on the entire course to give you more time to prepare for the final. 40% of the final grade. Grading. Workshops: 5%

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Physics 122

Lecture XXIV

Final exam
Final Exam

  • Saturday, December 17, 8:30 am (sorry!) - Hoygt

  • Final exam is based on the entire course PHY122.

  • Last homework will be based on the entire course to give you more time to prepare for the final.

  • 40% of the final grade

Lecture XXIV


  • Workshops: 5%

  • Homework: 5%

  • Hour Exams: 40%

  • Final Exam: 40%

  • Laboratory: 10%

  • Total: 100%

  • 90% or above: A 88-89.9 – A- 85-87.9 – B+

  • 80% - 85% : B 78-79.9 – B- 75-77.9 – C+

  • 70% - 75%: C 68-69.9 – C- 65-67.9 – D+

  • 60% - 65%: D

  • Under 60% : F

Lecture XXIV

Electricity and magnetism
Electricity and magnetism

  • The most important concept - electromagnetic field

  • First introduced for convenience

  • Electric charge changes the properties of space around them = creates electric field

  • Other charges feel this change  interaction between electric charges is mediated by the electric field

  • Change in electromagnetic field propagates with finite velocity (c ) = electromagnetic wave – proof that EM field is a reality

Lecture XXIV

Maxwell s equations constitution for em field
Maxwell’s equations = constitution for EM field

  • Gauss’ law – field lines start on + and end on -

  • No magnetic charge – closed field lines

  • Changing magnetic flux acts like a source of electric field

  • Amper’s law with extra term

Lecture XXIV

Gauss s law
Gauss’s law

  • Describes electric field created by electric charges

Lecture XXIV

Gauss coulomb
Gauss Coulomb

  • Calculate E of point like (+) charge Q

  • Consider sphere radius r centered at the charge

  • Spherical symmetry: E is the same everywhere on the sphere, perpendicular to the sphere

Lecture XXIV

Application of gauss s law
Application of Gauss’s law

  • Infinitely long thick charged wire, radius R

  • Charge per unit length Q/l=l

  • r>R:

  • r<R:

Lecture XXIV

Amper s law
Amper’s law

  • Describes magnetic field created by moving charges = currents

Lecture XXIV

Ampere s law
Ampere’s Law

  • In a way similar to Gauss’s law for E and Q

  • Not flux, integral over closed path

  • Only component of B parallel to dl contributes to integral

Lecture XXIV

Application of ampere s law
Application of Ampere’s Law

  • Thick wire of radius R carries current I. What is B(r ) in and outside of the wire?

  • Current through unit area:

  • Current through circle radius r<R

  • Path integral over radius r

  • Ampere’s law

  • For r>R – same as thin wire

Lecture XXIV

Forces on charges
Forces on charges

  • Maxwell’s equations tell us about the EM field

  • They tell nothing about the force that this field exerts on charges – Lorentz force

Lecture XXIV

Crossed fields
Crossed fields

  • Electric field changes kinetic energy of charged particle


  • Magnetic field does not change KE, only direction

  • Lorentz force:

  • Force due to E is parallel to E

  • Force due to B is perpendicular to B and to velocity of moving particle

Lecture XXIV

Motion in electric fields

a is always || to net F

Remember v is not always || to a (projectile, circular motion)

Motion in electric fields

- - - -



+ + + +



Lecture XXIV

Magnetic force on moving charge
Magnetic force on moving charge

  • Magnetic force F is perpendicular to the velocity v of a particle with charge q

    F=qvB sin q

  • Magnetic field does not change the magnitude of particle’s velocity, only its direction. Charged particles move in circles in constant magnetic field

Lecture XXIV

Magnetic force on moving charge1
Magnetic force on moving charge

  • Circular motion

  • Magnetic force = Centripetal force


  • Centripetal acceleration


  • Newton’s second law



In experiments B is known,

q=e most of the time,

Measure R- measure mv

For a given v measure m – magnetic spectrometer

Lecture XXIV

Cyclotron frequency
Cyclotron frequency

Frequency does not depend on v!

For a given particle type (q,m=const) it depends only on B

Lecture XXIV

Particle selector
Particle selector

  • Crossed E and B fields:

  • For one given velocity electric force exactly compensates magnetic force

  • Only particles with this value of velocity emerge from particle selector

+ + + +

- - - -


Lecture XXIV

Sources of e and b
Sources of E and B

  • Sources of E

    • Electric charges

    • Changing magnetic field

  • Sources of B

    • Currents

    • Changing electric field

  • In vacuum

    • No currents, no charges

Lecture XXIV

Radiation from an ac antenna
Radiation from an AC antenna

  • Changing electric field creates magnetic field

  • Changing magnetic field creates electric field

  • Change propagates with a finite velocity

  • Electromagnetic wave – proof of unification

Lecture XXIV

Em wave
EM wave

Lecture XXIV

Em wave1
EM wave

This is the speed of light!!!

Light is an EM wave!!!

Lecture XXIV

Energy in em wave
Energy in EM wave

  • EM waves transport energy

  • Energy density:

Lecture XXIV