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Unformatted text preview: Physics 212
Lecture 29
Course Review
• The Topics You Want to See
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– Electric Fields/Gauss’ Law/Potential (34%)
Faraday’s Law (12%)
RC/RL Circuits (14%)
AC Circuits (11%)
Geometric Optics (13%)
Magnetic Fields & Forces (7%)
Electromagnetic Waves/Polarization (8%)
DC Circuits (3%) Physics 212 Lecture 29, Slide 1 Music
Who is the Artist?
A)
B)
C)
D)
E) Marc Ribot
Marc Ribot
Bill Frisell
Bill Frisell
Jake Hertzog
Pat Metheny
Pat Metheny
John Scofield
John Scofield Why??
I think he is my favorite jazz guitarist !!
We bookend the course with incredible guitar players
Jeff Beck & Bill Frisell
Jeff
Frisell Physics 212 Lecture 29, Slide 2 BB E from top arc points down Horizontal components cancel E from bottom arc points up Top arc produces smaller horizontal components Etotal points down Calculation:
Etop = ∫ λ= dq
4πε0 r Q
2rθtop Etop = 2 θ cos θ Etop = Q sinθ
θ
1 4πε0 Q
r 2 2rθtop sin θtop 4πε0 r 2 θtop θ top 2 ∫ rdθ cos θ
0 θ
Physics 212 Lecture 29, Slide 3 BB Potential Energy is a measure of work done by E field
Spherical symmetry & Gauss’ law
law
E = 0 inside shell
inside E = 0 inside shell
inside
No work done to move q
No No change in potential energy !
Physics 212 Lecture 29, Slide 4 BB ALWAYS START
ALWAYS
FROM DEFINITION
OF POTENTIAL
OF
ar r
∆V = − ∫ E ⋅ dr
(A) 1 2Q 3Q − 4πε 0 a
b (B) 1 3Q 2Q − 4πε 0 b
a (C) 0 (D)
(E) 1 2Q 2Q − 4πε 0 a
b
1 2Q 2Q − 4πε 0 b
a 2Q
∆V = −
4πε0 b Spherical symmetry &
Spherical
Gauss’ law determines E
Gauss
1 2Q
a < r < b: E =
4πε0 r 2
a dr ∫2
br ∆V = 2Q 1 1 −
4πε0 a b Physics 212 Lecture 29, Slide 5 BB (A) 1 2Q 4πε 0 a (B) − (C) 0 1 2Q 4πε 0 a (E) Spherical symmetry &
Spherical
Gauss’ law determines E
Gauss
r < a: (D) E =0 1 3Q 4πε 0 b − 1 3Q 4πε 0 b ar r
∆V = − ∫ E ⋅ dr = 0
0 Physics 212 Lecture 29, Slide 6 Charge must be
Charge
induced to insure
E = 0 within
conducting shell
conducting BB Spherical symmetry &
Spherical
Gauss’ law determines E
Gauss
r r Qenclosed
∫ E ⋅ dA =
ε0
(A)
(B) − Q1
4πa 2
+ Q1
4πa 2 (C) (D) Q2 − Q1
4π (b − a )
2 2 (E) − Q1
4πb 2 E ⋅ 4πr 2 = 0 + Q1
4πb 2 Qenclosed = Q1 + (−Q1 ) σ= − Q1
4πb 2 Physics 212 Lecture 29, Slide 7 r < a: E = 0
Eliminate (a) and (c) BB b < r < c: E = 0
Eliminate (e)
a < r < b: E = kQ1/r2
r > c: E = k(Q1+Q2)/r2
Q1 = 3µC
Q1 + Q2 = +2µC
For r > c,
For
E must be less than the
continuation of E from a to b
continuation
Physics 212 Lecture 29, Slide 8 BB ALWAYS START
ALWAYS
FROM DEFINITION
OF POTENTIAL
OF
br r
∆V = − ∫ E ⋅ dr
0 Break integral into two pieces
ar r br r
∆V = − ∫ E ⋅ dr − ∫ E ⋅ dr
0
conductor: = 0
insulator: ∫ 0
insulator: a
same for
same
conductor
& insulator
insulator Physics 212 Lecture 29, Slide 9 1 L dI1
+ IR − V = 0
dt I – I1 I
I1 2 L dI1
− ( I − I1 ) R = 0
dt
IR = V − L 1
30% 2 L dI1
dI
− V + L 1 + I1R = 0
dt
dt 2L Strategy: Back to First Principles
• The time constant is determined from
The
a differential equation for the current
through the inductor.
through
• Equation for current through inductor
Equation
obtained from Kirchhoff’s Rules
obtained dI1
dt dI1
+ I1R = V
dt τ= " L" 2 L
=
" R" R Physics 212 Lecture 29, Slide 10
10 BB 76% Current induced because flux is changing
Flux is changing beause B is changing
Flux
beause
At t = 5 seconds, B is positive, but decreasing
Lenz’ law: emf induced to oppose change that brought it into being
law: emf
Induced current must produce positive B field
Positive B field produced by counterclockwise current
Physics 212 Lecture 29, Slide 11
11 BB 62% rr
Flux definition: Φ = ∫ B ⋅ dA = BA = Bwh
Faraday’s law: ε = −
dB
= −2T / s
dt dΦ
dB
= − wh
dt
dt
I= ε
R = 9/5
= .012 A
150
Physics 212 Lecture 29, Slide 12
12 BB 65% Current is determined by time rate of change of the flux
dΦ/dt is determined by dB/dt
dB/dt (6s) = dB/dt (5 s) = 2 T/s
(5
The induced currents at t = 5s and t = 6s are equal
Physics 212 Lecture 29, Slide 13
13 Phasor diagram at t = 0 What is VC at t = π/(2ω)
at
(A) α + VC max sin α (C) + VC max cos α (B) − VC max sin α (D) − VC max cos α BB Phasor diagram at t = π/(2ω)
diagram
VR α VC VL Voltage is equal to
Voltage
projection of phasor
phasor
along vertical axis
Physics 212 Lecture 29, Slide 14
14 ...
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This note was uploaded on 02/09/2012 for the course PHYSICS 212 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.
 Spring '11
 MESTRE
 Electric Fields, Force, Polarization

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