REVIEW FOR FINAL EXAM
December 2009
BASIC PHYSICS 218
COULOMB’S LAW
ELECTRIC FIELD
ELECTRIC FIELD LINES
1
Consider a ring of uniform charge
Find Ex at P
2
Where
Etc.
3
GAUSS’S LAW and ELECTRIC FLUX
Example 22.9
Positive electric charge Q is distributed uniformly
throughout the volume of an insulating sphere with radius
R.
a. Find the electric field at point p where r < R. b. Find the electric field at point p where r > R. 4
ELECTRIC POTENTIAL
ELECTRICAL POTENTIAL IS POTENTIAL ENERGY
PER UNIT CHARGE
POTENTIAL DIFFERENCE
5
Gauss’s Law
6
Choose
where
Example 23.11 Potential on axis of ring of
charge.
7
Find potential at P
ELECTRON VOLT
An electron volt is a unit for energy. It is
the work necessary to move an electron
(charge
) a potential
difference of 1 volt.
Capacitors
8
Parallel plate capacitors
But
C=?
9
Need
Gauss’s Law gives
10
CAPACITORS IN CIRCUITS
11
ENERGY IN CAPACITOR AND ELECTRIC FIELD
1
2
Use definition of capacitance
Or
Energy density
12
Therefore
DIELECTRICS
Add material between plates and C increases.
13
Current is the time rate of passage of the
charge.
RESISTIVITY of a material
RESISTANCE of an object
This is Ohm’s Law.
14
A copper rod with cross section A has a
length L what is its resistance?
Work for
and
.
Resistivity of Cu
Therefore
If have I and R will have power lost.
15
Circuit elements:
Other symbols
16
17
18
Consider the following circuit.
19
12
What is the current through the 6 Ω resistor?
20
KIRCHHOFF’S RULES
Junction Rule
The sum of the currents into a junction is
zero.
Loop Rule
The sum of the potential differences in a
loop is zero.
21
R-C CIRCUITS
22
Discharge C through R
23
MAGNETIC FIELD AND MAGNETIC
FORCES
24
25
26
27
28
MAGNETIC FLUX
Just like Electric Flux but with magnetic
field.
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MAGNETIC FIELD NEAR WIRE
CARRYING CURRENT.
30
Magnet Field from wire carrying current.
Again is a unit vector.
This equation is the Biot-Savart Law.
31
This is Ampere’s Law
Find the Magnetic Field inside (r < R) of a
conducting cylinder.
32
r
33
What is B in solenoid? (Use Ampere’s Law)
34
Magnetic Flux
If this flux changes an emf will
be induced in the area.
Faraday’s Law
35
36
Lenz’s Law – direction of emf
The direction of the induced emf is such that it tends to
produce a current that will create a magnetic flux to
oppose the change in magnetic flux through the loop.
37
If
is 1.0 A/s what is the emf in the loop?
38
Motional emf
Dx
39
40
Mutual Inductance
I1
#1
#2
I2
Then
is the Mutual Inductance
41
Faraday’s Law gives
42
Self Inductance
Thus
Faraday’s Law
43
Self-Induced emf
What is the inductance, , of the black coil?
Area
A
44
B
Ampere’s Law
45
Magnetic Field Energy
Consider the coil
46
What is stored energy in the black solenoid?
47
Put into equation for
1
2
1
2
Energy density
48
R-L Circuit
49
50
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Energy propagating with an EM Wave
We define a vector, the Poynting vector, to
be
The direction of the Poynting vector is the
direction of propagation of the wave.
The magnitude of the Poynting vector is the
energy per unit time per unit area (power per
unit area) delivered by the wave.
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