Electromagnetism and Light

Transcription

1 Electromagnetism and Light Monday Properties of waves (sound and light) interference, diffraction [Hewitt 12] Tuesday Light waves, diffraction, refraction, Snell's Law. [Hewitt 13, 14] Wednesday Lenses, polarization [Hewitt 14] Thurday Magnetic fields, forces and motors [Hewitt 11] Friday Magnetic induction, generators [Hewitt 11]

2 FRIDAY Magnetic force on a current How motors work. Generators/Faraday's law Quantum Mechanics?

3 Magnetism and Electromagnetic Induction He who controls magnetism controls the universe. Dick Tracy

4 Electricity Positive charges emit electric fields, neg. charges absorb field lines. Magnetism North poles emit field lines, south poles absorb them. Charges feel electric Fields whether the charges Are moving or not. Only moving charges or currents Feel magnetic fields F =q E F =q v B B F =I L

5 Magnetic force on a charge > F=q v B Magnetic force on a current > F=I L B The second equation applies to most technology mostly in science do you have particles floating around outside of wires.

6 Magnetism and Electromagnetic Induction

7 Magnetism and Electromagnetic Induction

8 The right hand rules! You can get by with two. 1) For magnetic field around a current. 2) For cross products and everything else!

9 Let's do the force on an electron beam Electrons move to the right and you point the north pole of a magnet at them (into the page). The beam moves down! v F =q v B F

10 Magnetic field of a wire encircles the current. 0 I For infinitely long wire > B= 2 d

11 In standard household wiring, parallel wires about 1 cm apart carry currents of about 15 A. What is the magnetic field at 1 cm? What is the magnitude of the force per Unit length between the wires? 0 I B= 2 d 0 L 2 F= I 2 d F=I L B

12 Like currents attract DEMO

13 Torque on a current loop is proportional to magnetic moment. = B =I A

14 An electric motor is made from 100 turns of Copper wire in a square 10 cm on a side. It is placed in a 10 millitesla magnetic field. What is the maximum force one side of the square with a 100 amp current? (A) (B) (C) (D) (E) N 0.01 N 0.1 N 1N 10 N

15 An electric motor is made from 100 turns of Copper wire in a square 10 cm on a side. It is placed in a 10 millitesla magnetic field. What is the maximum torque with a 100 amp current? (A) (B) (C) (D) (E) N m 0.01 N m 0.1 N m 1 N m 10 N m = B =I A

16 Electric Motor demonstrations DC Electric Motor Brushless Motor Homopolar motor The simplest motor of the world Tinyurl.com/HomoMotor1

17 Why is magnetic dipole moment a useful concept? It's good for understanding motors. Protons and electrons have dipole moments. This is particularly surprising since electrons have zero size. Even at the quantum level, particles act like spinning balls of charge! MRI works by flipping over every proton in the Water molecules in your body!

18 MRI Used to be called Nuclear Magnetic Resonance (NMR) Protons are flipped by a resonant magnetic field. They flip back to align with the large axial (solenoid) field. The time it takes them to flip back is converted to shades of grey in the MRI image. The time is weakly affected by the type of tissue that surrounds them.

19 Magnetic Poles CHECK YOUR NEIGHBOR Wire A having 10 Amps runs current parallel to wire B carrying 20 Amps. Which wire feels the greater attractive force? A. B. C. D. A B Forces are the same none of the above

20 Magnetic Poles CHECK YOUR NEIGHBOR Wire A having 10 Amps runs current parallel to wire B carrying 20 Amps. Which wire feels the greater attractive force? A. B. C. D. A B Forces are the same Newton's third law is true even if you don't know ANYTHING about magnetism... none of the above 0 L F= I 1 I2 2 d

21 Given a magnetic field of 2 Tesla, what is the net force on the circuit shown? F=I L B [A ] F=4 A [B] F=0.4 N [C] F=8.0 T [D] F=8.0 N [E] F=0.8 N

22 A generator is a motor run backwards. Motor Apply current to wires in a magnetic field and create a force which will move the wires. Generator Move wires in a magnetic field by applying a force and the the field will induce a voltage on the wires V gen

23 Ampere's Law A constant current will produce a constant magnetic field, and a changing current will produce a changing magnetic field. Faraday's Law Generator Move wires in a magnetic field by applying a force and the the field will induce a voltage on the wires

24 zazzle.com cosmic_physics Faraday's Law Ampere's Law

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26 Faraday's Law What's a Flux? Field x Loop Area Changing magnetic fluxes produce electric fields and hence voltages (Vgenerator). B A V gen= Faraday 's Law t

27 Ways to change flux Can move loop into stronger or weaker B. Can increase/decrease B. Can rotate B. Can increase/decrease size of loop. Can rotate loop.

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29 Changing Flux by Changing B field

30 Changing Flux by Changing size Of Loop

31 Changing Flux by Changing size Of Loop Given B=0.1 T, l =0.1 m, v=20 m/s, R=30 Ohms, What are V, I, and P?

32 Changing flux by rotating loop

33 Changing flux by rotating loop

34 Was Newton wrong? Science operates in different regimes. A theory may work well in one regime but not another. Newtonian mechanics works well for objects larger than a few nanometers. Quantum mechanics is more general, but so complex for large systems that it is still much easier to use Newtonian mechanics when you can.

35 Why do we need quantum mechanics The light from hot bodies (light bulbs) could not be explained classically The photoelectric effect could not be explained classically The spectrum of hot atoms could not be explained. The mere existence of stable atoms should be impossible by E&M.

36 Classically light can have any amount of energy. Make it dim and energy goes to zero. In quantum theory, the smallest amount of energy you can have in light is one particle (quantum). A quantum of light is called a photon. Its energy is given by c Energy=E=h f =h ( ) λ 34 h= J s Planck's constant

37 Energy of a photon of green light? c Energy=E=h f =h ( ) 34 h= J s 8 34 E=( (3 10 m /s) 19 J s) = J 7 (5 10 m) One electron volt (ev)=( ( J) E= =2.48 ev 19 ( J / ev) 19 C)(1 Volt)

38 Bohr Wavelengths hc 1 1 E= =[13.6 ev ]( 2 2 ) n1 n 2 1 [13.6 ev ] 1 1 = ( 2 2 ) hc n1 n =R ( 2 2 ) n1 n R=Rydberg Constant= m =R ( 2 2 )=R ( )= R λ = =486 nm 42 3R

39 Why do we see spectral lines and not a continuous spectrum?

40 Bound electrons act differently than free electrons 2 e 1 1 Energy= ( 2 2) 4 π ϵ0 (2 a 0 ) n 1 n 2

41 Bohr Energies 2 e 1 1 Energy=[ ]( 2 2 ) 4 0 (2 a 0 ) n 1 n 2 19 e= C 12 0 = a 0 =0.53 nm F/ m 1 1 E=[13.6 ev ]( 2 2 ) n1 n 2

42 But what's REAL Quantum Mechanics Particles are described by probability waves. The average or most likely value of their position or Energy can be described by a Wave function and calculations are done on that function to measure the position of the particle.

43 Schroedinger's Equation Starts with classical energy. Tot. Energy=E=Kinetic Energy Potential Energy k q 1 q2 E=1/2 m v r 2 2 p kq E= 2m r p i ℏ kq ℏ 2 =E 2m r

44 Full form of Schroedinger's Equation for Hydrogen in spherical coordinates. 2 2 kq ℏ 2 =E 2m r 2 2 kq ℏ 2 =E 2m r L ℏ 2 ℏ 1 2 = r 2 2m 2m r r r 2mr L =ℏ [ sin 2 ] 2 sin sin

45 Solutions to Schroedinger's Equation for Hydrogen =R nl r Y lm,

46 Radial Solutions to Schroedinger's Equation for Hydrogen =R nl r Y lm, Note for larger n the electron IS farther from the nucleus.

47 Angular Solutions to =R nl r Y lm, Schroedinger's Equation

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49 Wave Barriers and Bow Waves Wave barrier waves superimpose directly on top of one another producing a wall example: bug swimming as fast as the wave it makes

50 Wave Barriers and Bow Waves Supersonic aircraft flying faster than the speed of sound Bow wave V shape form of overlapping waves when object travels faster than wave speed an increase in speed will produce a narrower V shape of overlapping waves.

51 Shock Waves and the Sonic Boom Shock wave pattern of overlapping spheres that form a cone from objects traveling faster than the speed of sound

52 Sonic Boom Shock wave consists of two cones a high pressure cone generated at the bow of the supersonic aircraft a low pressure cone that follows toward (or at) the tail of the aircraft it is not required that a moving source be noisy Why does the air condense?

53 Cerenkov Radiation and Tachyons Particles traveling faster than light make a shock wave too! Fast charged particles in the water bath of a nuclear reactor make a blue glow. Tachyons would glow in a vacuum