1. Review
Physics 122
11/10/2018
Lecture XXIV

2. 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
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3. Grading Workshops: 5% Homework: 5% Hour Exams: 40% Final Exam: 40%
Laboratory: 10%
Total: %
90% or above: A – A – B+
80% - 85% : B – B – C+
70% - 75%: C – C – D+
60% - 65%: D
Under 60% : F
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4. 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
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5. 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
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6. Gauss’s law Describes electric field created by electric charges
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7. 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
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8. Application of Gauss’s law
Infinitely long thick charged wire, radius R
Charge per unit length Q/l=l
r>R:
r<R:
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9. Amper’s law
Describes magnetic field created by moving charges = currents
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10. 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
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11. 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
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12. 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
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13. 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
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14. Motion in electric fields
a is always || to net F
Remember v is not always || to a (projectile, circular motion) vx vy
vx=const
vy=at=tF/m=tEq/m
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Lecture XXIV

15. 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
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Lecture XXIV

16. 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
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17. Cyclotron frequency Frequency does not depend on v!
For a given particle type (q,m=const) it depends only on B
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18. 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 +
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19. Sources of E and B Sources of E Sources of B In vacuum
Electric charges
Changing magnetic field
Sources of B
Currents
Changing electric field
In vacuum
No currents, no charges
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20. 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
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21. EM wave
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22. EM wave This is the speed of light!!! Light is an EM wave!!!
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23. Energy in EM wave EM waves transport energy Energy density: 11/10/2018
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24. 11/10/2018
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