Electromagnetism and LightMonday – 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] 

FRIDAY

Magnetic force on a currentHow motors work.

Generators/Faraday's law

Quantum Mechanics?

Magnetism and Electromagnetic Induction

“He who controls magnetism controls the universe.”    

 —Dick Tracy

Electricity           Magnetism

Positive charges emit                    North poles emitelectric fields, neg. charges          field lines, southabsorb field lines.                         poles absorb them.

Charges feel electric  Only movingFields whether the charges charges or currentsAre moving or not. Feel magnetic fields

F=q E F=q v×BF=I L×B

F=q v×BMagnetic force    ­­­>on a charge

Magnetic force    ­­­>on a current

The second equation applies to mosttechnology … mostly in science do you haveparticles floating around outside of wires.

F=I L×B

Magnetism and Electromagnetic Induction

Magnetism and Electromagnetic Induction

The right­hand rules!

You can get by with two.

1) For magnetic field around a current.2) For cross­products and everything else!

Let's do the force on an electron beam 

Electrons move to the rightand you point the north pole of a magnet atthem (into the page).

The beam moves down! F=q v×B

v

F

Magnetic field of a wire encircles the current.

For infinitely long wire ­­>  

B=0 I

2d

F=I L×BB=0 I

2d

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 perUnit length between the wires?

F=0 L

2dI2

Like currents attract …

DEMO

=×B

=I A=I A

Torque on a current loop is proportional to magnetic moment.

An electric motor is made from 100 turns ofCopper 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)  0.001 N(B)  0.01 N(C)  0.1 N(D)  1 N(E)  10 N 

An electric motor is made from 100 turns ofCopper 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)  0.001 N­m(B)  0.01 N­m(C)  0.1 N­m(D)  1 N­m(E)  10 N­m 

=×B

=I A

Electric Motor demonstrations

DC Electric Motor

Brushless Motor

Homopolar motor “The simplest motor of the world”

http://www.youtube.com/watch?v=zOdboRYf1hM&NR=1Tinyurl.com/HomoMotor1

http://www.youtube.com/watch?v=FjNnRyLexNMHttp://tinyurl.com/DCMotor2

http://www.youtube.com/watch?v=F9CPX3EJoN4

http://tinyurl.com/brushlessmotor1

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 Water­molecules in  your  body!

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.

Wire A having 10 Amps runs current parallel to wire B carrying 20 Amps.   Which wire feels the greater attractive force?

A. AB. BC. Forces are the sameD. none of the above

Magnetic PolesCHECK YOUR NEIGHBOR

Wire A having 10 Amps runs current parallel to wire B carrying 20 Amps.   Which wire feels the greater attractive force?

A. AB. BC. Forces are the same   Newton's third law is true even if you ←

don't know ANYTHING about magnetism...D. none of the above

Magnetic PolesCHECK YOUR NEIGHBOR

F=0 L

2dI1 I2

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

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  Vgen

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 

Ampere's Law

Faraday's Law

zazzle.com cosmic_physics

Faraday's Law

What's a Flux? Field x Loop Area

Changing magnetic fluxes produce electric fields and hence voltages (Vgenerator).

Vgen=−BA

t Faraday 's Law

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.

  

Changing Flux by Changing B­field

  

Changing Flux by Changing sizeOf Loop

  

Changing Flux by Changing sizeOf Loop

Given B=0.1 T, “l”=0.1 m, v=20 m/s, R=30 Ohms, What are V, I, and P?

  

Changing flux by rotating loop

  

Changing flux by rotating loop

  

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.

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.

Energy=E=h f=h (cλ )

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

← Planck's constanth=6.62×10−34 J⋅s

Energy=E=h f=h (c)

Energy of a photon of green light?

h=6.62×10−34 J⋅s

E=(6.62×10−34 J⋅s)(3×108 m /s)

(5×10−7 m)=3.97×10−19 J

One electron−volt (eV)=(1.6×10−19 C)(1 Volt)¿

E¿

=(3.97×10−19 J)

(1.6×10−19 J /eV)=2.48 eV

Bohr Wavelengths

E=hc=[13.6 eV ](

1

n12−

1

n22)

1=[13.6 eV ]

hc(

1

n12−

1

n22)

1=R (

1

n12−

1

n22)

R=Rydberg Constant=1.097×107

m1λ42

=R (1

22−1

42 )=R (14−

116

)=3

16R

42=163 R 42=486 nm

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

Bound electrons act differently than free electrons

Energy=e2

4πϵ0(2 a0)(

1

n12−

1

n22) Http://tinyurl.com/bohratom

Bohr Energies

Energy=[e2

4 0(2 a0)](

1

n12−

1

n22)

e=1.6×10−19 C

0=8.86×10−12 F /ma0=0.53 nm

E=[13.6 eV ](1

n12−

1

n22)

Http://tinyurl.com/bohratom

But what's REAL Quantum Mechanics

Particles are described by probabilitywaves.

The average or most likely value oftheir position or Energy can bedescribed by a “Wave function” andcalculations are done on that functionto “measure” the position of theparticle.

Schroedinger's Equation

Starts with classical energy.

Tot. Energy=E=Kinetic EnergyPotential Energy ¿

E=1/2 m v2

k q1 q2

r

E=p2

2m

kq2

rp−i ℏ ∇

−ℏ2

2m∇

2

kq2

r=E

Full form ofSchroedinger's Equation for Hydrogenin spherical coordinates.

−ℏ2

2m∇

2

kq2

r=E

−ℏ2

2m∇

2

kq2

r=E

−ℏ2

2m∇

2=−ℏ

2

2m1

r2∂∂ r

r2 ∂∂ r

L2

2mr2

L2=ℏ

2[

1sin

∂∂

sin ∂∂

1

sin2

∂2

∂2]

Solutions to Schroedinger's Equation for Hydrogen

=Rnl rY lm ,

Radial Solutions to Schroedinger's Equation for Hydrogen

Note for larger nthe electron ISfarther from thenucleus.

=Rnl rY lm ,

Angular Solutions to Schroedinger's Equation

=Rnl rY lm ,

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

Wave Barriers and Bow Waves

Supersonic aircraft flying faster than the speed of soundBow wave V­shape form of overlapping waves when object 

travels faster than wave speed an increase in speed will produce a narrower  V­

shape of overlapping waves.

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

Sonic BoomShock wave consists of two cones

a high­pressure cone generated at the bow of the supersonic aircraft

a low­pressure 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?

Cerenkov Radiation and Tachyons

Particles traveling faster than light make a shock wave too!

Fast charged particles inthe water bath of a nuclear reactor make a blue glow.

Tachyons would glow in a vacuum