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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

Grading

- 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

- 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

- 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 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

- Infinitely long thick charged wire, radius R
- Charge per unit length Q/l=l
- r>R:
- r<R:

Lecture XXIV

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

- 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

- 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

- Electric field changes kinetic energy of charged particle
qDV=mv2/2

- 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

a is always || to net F

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

Motion in electric fields- - - -

vx

vy

+ + + +

vx=const

vy=at=tF/m=tEq/m

Lecture XXIV

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 charge

- Circular motion
- Magnetic force = Centripetal force
F=qvB

- Centripetal acceleration
a=v2/R

- Newton’s second law
F=ma

qvB=mv2/R

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

Frequency does not depend on v!

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

Lecture XXIV

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
- 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

- 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

Lecture XXIV

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