Welcome to Physics 7C!Welcome to Physics 7C!

Lecture 6 -- Winter Quarter -- 2005

Professor Robin Erbacher

343 Phy/Geo

erbacher@physics.ucdavis.edu

AnnouncementsAnnouncements

• Course policy and regrade forms on the web: http://physics7.ucdavis.edu

• If you received rubric code 4 on part b) of Quiz 2, please hand in your quiz for a possible regrade.

• Quiz today on Block 13, DLMs 9 and 10.

• Block 13 continues: DLMs 11 and 12 this week.

• 3 DLs canceled on Thursday: 10:30, 4:40, 7:10.

• Turn off cell phones and pagers during lecture.

Gradients: Potential Energy Gradients: Potential EnergyRecall: What is the potential energy of a mass m in a the Earth’s gravitational field, a height h above the surface of the Earth?

PE = mgh !• Force on a mass m in gravity field g is F = mg.• Magnitude of force is the spatial derivative, or gradient, of the potential energy of the mass:

€

Fon m = -d

drPE gravity( )

€

PE gravity = GMm

r

The direction of the force on the mass m is toward decreasing PEgrav (hence the negative sign!)

Gradientrelation

Gradients for E Fields: Potential

Gradients for E Fields: Potential

Analogous to the gravitation case:• Force on a charge q in an Electric field E is F = qE.• Magnitude of force is the spatial derivative, or gradient, of the potential energy of the mass:

€

Fon q = -d

drPE electric( )

€

PE electric = - kQq

r

The direction of the force on the charge +/- q is toward decreasing PEgrav (hence the negative sign again!)

Electric Potential VElectric Potential V• Electric potential V depends on position, and distances.• The electric field E can be determined by the spatial derivative of an electric potential, V.

€

Felectric = −Δ PE electric( )

Δx,

Felectricq

= −

ΔPE electricq

⎛

⎝ ⎜

⎞

⎠ ⎟

Δx,

E = −Δ V( )Δx

.

PE = qV

+-E

+q

What is the changein potential energy ifthe charge +q movesfrom the positive plateto the negative plate?

We need more information: distancebetween the plates, voltage drop across the capacitor, …

Magnetic Fields and ForcesMagnetic Fields and ForcesAnalogy to Gravity/Electric fields: Magnetic Fields

We can think about moving charge I (current) exerting a force on a moving charge qv.

€

Fdirect

magnitude = qvμ0I

2πrObject A Object B

exerts force

Direct Model of Forces

€

Ffield = qv ×μ0I

2πr

⎛

⎝ ⎜

⎞

⎠ ⎟ = qv × B

field Object B

exerts forceObject A field

creates

Field Model of Forces

Magnetic Field BMagnetic Field BWe have now derived the magnetic field B, which exists in the presence of moving charge (or current) I :

What does B depend on? What units does it have?

In which direction does it point?

€

B = μ0I

2πr

⎛

⎝ ⎜

⎞

⎠ ⎟Magnitude of

magnetic field:

1/r …and current I Teslas

I

B

Right hand rule

for B field vectors

(RHR1)

Electric and Magnetic Field Maps

Electric and Magnetic Field Maps

E field

vectors

B field

vectors

stationary

+ Q line

stationary

+ Q line

moving

+ Q line

E field

vectors

B field

vectors

moving

+ Q line

Force due to B FieldForce due to B Field

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The force on a moving charge dueto a B field is:

€

Ffield = qv ×μ0I

2πr

⎛

⎝ ⎜

⎞

⎠ ⎟ = qv × B

What direction is the resulting force? (What is this cross-product thing?)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The Hall Effect (1897)

v

F

B

F

v

B

F

v

B

θ

F = 0

v

Bθ

€

A ˆ x × B ˆ y = C ˆ z

€

qv ˆ x × B ˆ y = Fˆ z

€

Magnitude Ffield = qvBsinθ

Electrons as ParticlesElectrons as ParticlesWe know that moving electric charges cause magnetic fields. Another source of magnetism can be “spin”.

• Electrons orbiting nuclei create current loops• Protons and electrons themselves have rotation: Spin!

The electron is a source of both

an electric field (due to its

negative charge) and a

magnetic field (due to its "spin")

E B

e ﾐ e ﾐe- e-

1s

2s

2p

3s

3p

4s

3d

Hund's Rules for Fe 2+

2

2

6

2

6

2

4

Hund’s Rules for electron shells levels:Electrons pair up and cancel out magnetic Properties. Leftover electrons can giveMore magnetic properties, like with Fe2+.

Harmonic Waves and LightHarmonic Waves and LightElectric and magnetic fields are everywhere surrounding charges. If we send them into simple harmonic motion, the fields fluctuate in a spatially and time-varying way.

This is light! An electromagnetic (EM) wave!

E ( z ) at a particular t

x �

y �

z �

y

€

Ey z ,t( ) = Ey,max sin2πt

Τ±

2πz

λ+ψ

⎛

⎝ ⎜

⎞

⎠ ⎟,

Bx z ,t( ) = Bx,max sin2πt

Τ±

2πz

λ+ψ

⎛

⎝ ⎜

⎞

⎠ ⎟.

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

Alternating Currents (AC)Alternating Currents (AC)As you see in DLM 11, you induce a current by movinga loop through a B field. The current acts to oppose a change in B field through the loop.

Lens’ Law! The current changes direction as you move in and out.

B field

wire loop

(a)

B field

(b)

B field

(c)

Our regular household power is 110V AC. (Can get 220V, multi-phasic, etc). What does DC mean?