Physics 7C, Lecture 5 Winter Quarter -- 2007 Electric Potential, Magnetism, Magnetic Forces...
-
date post
21-Dec-2015 -
Category
Documents
-
view
250 -
download
8
Transcript of Physics 7C, Lecture 5 Winter Quarter -- 2007 Electric Potential, Magnetism, Magnetic Forces...
Physics 7C, Lecture 5Physics 7C, Lecture 5
Winter Quarter -- 2007Winter Quarter -- 2007
Electric Potential, Magnetism,
Magnetic Forces
Professor Robin Erbacher343 Phy/Geo
AnnouncementsAnnouncements
• Course syllabus (policy, philosophy) on the web: http://physics7.ucdavis.edu
• Unit 9 continues today: DLMs 8 -14.
• Quiz #3 today, on optics and electric fields/forces. • Quizzes every other lecture, ~20 minutes each, average of 4 best = 45% (or 20)% of grade.
• Turn off cell phones and pagers during lecture.
Gradient Relations: Potential Energy
Gradient Relations: Potential Energy
Recall: 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
Gravitational Potential EnergyGravitational Potential Energy
Force increases with greater slope
Pote
ntia
l Energ
y d
iffere
nce
r
-
0
PE = GMm/r
F = - PE/r, the - slope
Negative means rapid decrease of PE with decreasing r
Gradients for E Forces: Potential Energy
Gradients for E Forces: Potential Energy
• 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 charge:
€
Fon q = -d
drPE electric( )
€
PE electric = - kQq
r
Fon q due to Q = kQq
r2 = qE
E due to Q = kQ
r2
The direction of the force on the charge +/- q is toward decreasing PEcharge (hence the negative sign again!)
Gradients for E Fields: Electric Potential
Gradients for E Fields: Electric Potential
• Slope of the Electric Potential•Constant with distance•Negative
• Electric field is•Constant as a function of distance•Positive
1 :
ˆ ˆ ˆ3 :
dVD E
dxdV dV dV
D E x y zdx dy dz
→
→
=−
=− − −
Electric Potential V (voltage)
Electric Potential V (volts)Electric Potential V (volts)
• Electric potential V depends on position, and distances.• The electric field E can be determined by the spatial derivative of an electric potential, V.
Equipotential surfaces for point charge: Lines where V is the same.
• Circles are 0.5 volts apart, but distances between are NOT uniform.
• Circles get closer and closer toward center. • Potential grows as 1/r.
• Field lines perpendicular to equipotential surfaces.• Electric Field points in direction of decreasing potential.
VE
s
=−
Electric potential of point charges
Electric potential of point charges
• We lose kinectic energy as we get closer, until we stop and rebound
Positive charge: potential hill Negative charge: potential well
• We gain kinectic energy as we get closer, it pulls us in!
Recall: Electric Field of a DipoleRecall: Electric Field of a Dipole
From Lecture 4:Continuous field lines
Topographical Maps: Lines of Equal Elevation
Topographical Maps: Lines of Equal Elevation
3 Views of Mt. Fuji.
Dipole Equipotentials: A “topo” map for electricityDipole Equipotentials: A
“topo” map for electricity
Which direction does the E field point at P?
a) E=0b) To the rightc) To the leftd) Out of page
PRS question:
P
Surface plot: potential for a dipole
Surface plot: potential for a dipole
+ Chargecauses a “hill”
- Chargecauses a “hole”
Review: force, fields, potential energy, potential
Review: force, fields, potential energy, potential
Force Field Pot. Energy Potential
Force AND field arein the direction ofdecreasing PE and
Newtons N/kg Joules (Nm) Joules/kg(kg m/s2) N/C eV Volts
units
2
2
r
kQE
r
GMg
=
=
r
r rfield
r
1∝
F
rq
r
PEEq
rm
r
PEgm
elecelec
gravgrav
−=
−=
−=
−=
r
r
Magnetic FieldsMagnetic Fields
The sun is not a static object, it sometimes can hurl a large amount of particles out into space. These charged particles would quickly erode our atmosphere, but thankfully, Earth’s magnetic field protects us from this solar “coronal mass ejections”. A large part of what makes Earth hospitable is the magnetic field, it is effectively a shield that protects our atmosphere.
Bar magnetsBar magnets
If allowed, bar magnets will always point north or south.
SN
Bar magnets attract one end of a compass needle and repulse the other.
Magnets have poles that attract and repel.
S N S N
S N SN
Earth’s Magnetic FieldEarth’s Magnetic Field
Magnetic Field LinesMagnetic Field Lines
Magnetic Charge?Magnetic Charge?
Some objects can be picked up by magnets, not all.
Iron, nickel, and cobalt are common magnetic materials, copper, aluminum, glass, and plastic are not.
Ends of an attracted object will be attracted.
What happens when a charged object is brought near a magnet?
a) The south pole goes toward the positive
b) The north pole rotates toward the positive
c) Neither pole is attracted. The magnet won’t rotate
Nature tells us electricity and magnetism are related, but not like this.Magnetism is an entirely new type of phenomena.
There is no such thing as a magnetic charge! (monopole)
PRS question:
Inferring a Field…Inferring a Field…
In 1820, a Dane by the name of Hans Christine Oersted discovered that when you bring a compass near a wire carrying current something very interesting happens.
Compasses near a wire…Compasses near a wire…
Faraday’s “field” Faraday’s “field”
Patterns like these led to Faraday’s concept of the field.
Moving Charges Magnetic Fields!
Moving Charges Magnetic Fields!
B-field vectors
I
If a charge (or charges) move, as in a current I, a magnetic vector field B is always induced around the current.
The Magnetic Field BThe Magnetic Field BWe have now deduced the existence of a magnetic field B in the presence of moving charges (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)
r
IB
IB
IdB
enclosed
enclosed
πμ
μ
μ
20
0||
0
=
=
=•
∑∫
r
l
lrr
Ampere’s Law:
B
Direction of B field, RHR1Direction of B field, RHR1
BI
To get direction, use right hand rule #1:
Point thumb of RH along direction of current I. Fingers are now curling in direction of B field.
B field from aboveB field from above
Circles around and weakens with increasing r
Current is going toward you
B-field vectors
B = μI
2πr
B directly depends on strength of current
Finding field directionsFinding field directions
Where does the field vector point at spot P?
1) Into the screen
2) Out of the screen
3) Towards the wire
4) Away from the wire
5) Points down
6) Points up
7) Another direction I
P B
W
PRS question:
Finding field directionsFinding field directions
I
P N
W
PRS question:
Where does the field vector point at spot N?
1) Into the screen
2) Out of the screen
3) Towards the wire
4) Away from the wire
5) Points down
6) Points up
7) Another direction
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
Recall: Force ModelsRecall: Force ModelsRecall our discussion about contact forces, used when direct action occurs between 2 bodies. We called this: Direct Model of Forces
But when we considered questions of indirect forces:How does Earth exert its gravitational force on the ball while in mid-air?
This was an example of action-at-a-distance, leading toField Model of Forces
€
Object A Object B
exerts force
field Object Bexerts forceObject A field
creates
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
Electric and Magnetic Field Maps
Electric and Magnetic Field Maps
Charge creates a field that puts a force on other charges.
Moving q B field force on other moving charges, qv
Moving charge, or a current of moving charge, creates a field that places a force on moving charge. This is a different field than the static E-Field and creates a different type of force. This is an empirical finding.
All charges create E-fields but only moving charges create B fields!
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
Right-hand rule 2!
Finding Magnetic ForceFinding Magnetic Force
I
P N
W
PRS question:
What direction is the force F on a charge +q with velocity v at point N?
1) Into the screen
2) Out of the screen
3) Towards the wire
4) Away from the wire
5) Points down
6) Points up
7) Another direction
+qv
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?