Download Physics 231 Course Review, Part 3

Important Concepts
1.
2.
3.
4.
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6.
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8.
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14.
15.
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21.
22.
Coulomb’s Law
Electric Fields
Electric Field Lines
Electric Fields in Conductors
Electric Flux
Gauss’s Law
Electric Potential Energy
Electrostatic Potential
Equipotential Lines
Capacitance
Resistance and Ohm’s Law (series & parallel)
Kirchhoff’s Laws
RC Circuits
Magnetic Force on Particle – RHR
Magnetic Force on Conductor
Sources of Magnetic Fields Law of Biot-Savart
Magnetic Flux – Ampere’s Law
Magnetic Flux – Induction (Faraday & Lenz)
Inductance
RL Circuits
RC Circuits
AC Circuits
13. RC Circuits
Example 2 – Discharging a Capacitor-
+
q = Q0 e − t / RC
Mr. Kirchhoff says:
q
iR + = 0
C
I = I 0 e −t / RC
Exponential Decay – Which Curve is right?
Strategy for understanding which curve is correct:
Try to figure out what the current (or charge) would be just when
the switch is closed (or opened)
t=0
Then try to figure out what the current (or charge) would be after
a very long time
t=∞
I8 =0
the capacitor is fully charged and there
is no current:
I0=ε/R
At t=0 there is NO charge on the capacitor –
and therefore no voltage across capacitor
I0
At t=8
I0
F = q vB⊥
r
r r
F = qv × B
15. Magnetic Force on a Charged Particle
Units of Magnetic Field:
1 Tesla = 1 T = 1 Newton/(Ampere·meter)
r r
v
C
r = A B sin θ ,
r
B . The direction of C
The “Vector” or “Cross Product”
v r r
If C = A × B then the magnitude
r of
where θ is the angle between A and
is given by the “Right Hand Rule”:
Advice on using the Right Hand Rule:
1) First determine the plane that contains A and B. The cross product will
point perpendicular to that plane. There are only two choices.
2) Use the Right Hand
r Ruler to rpick which choice is correct.
3) If you are using F = qv × B , Remember that a negative charge will reverse
the direction of the cross product!
15. Magnetic Force on a Conductor
16. Sources of Magnetic Fields
Force between two infinite conductors
17. Magnetic Flux – Amperes Law
The sign of the line integral gives the direction of the current
Step 1: Curl the fingers of your RH in the direction of Integration
Step 1: If Integral > 0, then current flows in the direction of thumb
I
Step 1: If Integral < 0, then current flows in the direction
opposite that of the thumb
I
Electromagnetic Induction
18.Concept
Magnetic Flux
– InductionFlux
Key
is Magnetic
Faraday’s Law
r r
dΦ B where Φ =
B ⋅ dA = ∫ BdA cos φ
B
∫
ε =−
surface
surface
dt
It doesn’t matter why the flux changes
1) Constant B, Changing Area:
2) Constant Area, Changing B:
3) Constant Area, Constant B, Changing Cos φ:
Induced Electric Fields
Faraday’s Law hold even if there is
no Motion and no Magnetic Field
Φ B = BA = µ0 nIA
dΦ B
dI
= − µ0 nA
dt
dt
Faraday’s Law implies that there is an
“Induced” Electric Field
ε =−
r r
∫ E ⋅ dl = ε
r r
dΦ B
∫ E ⋅ dl = − dt
This “Induced” Electric Field is a
non-electrostatic field that arises,
not from static charges, but from a
changing B field alone.
Direction of the Induced EMF’s and Currents
In the previous problem, we found the direction
of the induced current by noting that the force
resulting from the induced current had to
oppose the applied force. This obbservation can
be generalized into:
Lenz’s Law
The direction of any magnetic induction effect
is such as to oppose the cause of the effect
19. Inductance
Mutual Inductance
SELF-INDUCTANCE
20. RL Circuits
Discharging:
21. The L-C Circuit
x = A cos(ωt)
ω stays constant
A changes
A stays constant
ω changes
Representation of Sinusoidal Motion
Using Rotation of a “Phasor”
Current and Voltage in AC Circuits
Frequency Dependence of Resistance and Reactance