Unformatted text preview: Physics 212
Lecture 22 Physics 212 Lecture 21, Slide 1 Music
Who is the Artist?
A)
B)
C)
D)
E) Billy Joel
Boz Scaggs
Mark Knopfler
Mark Knopfler
Donald Fagen
Donald Fagen
Michael McDonald 1976 Video
2004
Great band.. Good blues
1994 Theme of the week?
Bay Area Memories.. Slim’s?
Bay
Slim
p.s. I had another good idea, but I forgot to load it on my ipod last night!!
p.s.
ipod
Physics 212 Lecture 21, Slide 2 Your Comments
“You lied about electric potential being the hardest part of the
You
course! Please go through everything in detail because this is a
course!
confusing prelecture and I don't understand most of it at all.
confusing prelecture
“I feel like I don't understand this well enough to even
feel
ask questions about it. Little bit shellshocked right now.”
ask
“THAT WAS AWESOME!! DISCUSS ALL PLEASE!!!! “
“wave equations, this is my first time seeing them
wave
(aside from oscillators)”
(aside
“more about the graphs of waves. they are confusing”
“Do we have to know how to solve differential
Do
equations or will the problems be limited to these
specific types of examples?”
specific ALL TRUE
We will try to
We
make clear,
at least the
BIG IDEAS
BIG We will discuss waves
We
You will not have to
solve new diff eqns
eqns 40
30
20 “How can light act as both a wave and a particle?”
PHYS 214 Ø PHYS 419
PHYS 10
0 05 Confused Confident Physics 212 Lecture 21, Slide 3 What We Knew Before Prelecture 22 06 Physics 212 Lecture 21, Slide 4 After Prelecture 21: Modify Ampere’s Law
After Prelecture
σ
Q
E= =
ε0 ε0 A Φ = EA = Q ε0 Q = ε 0Φ
dQ
dΦ
= ε0
≡ ID
dt
dt 10 Physics 212 Lecture 21, Slide 5 Displacement Current
Real Current: Charge Q passes through area A in time t:
I= Displacement Current: Electric flux through area A changes in time
ID = ε0 08 dQ
dt
dΦE
dt Free space Physics 212 Lecture 21, Slide 6 Calculation
Switch S has been open a long time when at t = 0, it is closed.
Capacitor C has circular plates of radius R. At time t = t1, a
V
current I1 flows in the circuit and the capacitor carries
charge Q1. S
C
Ra At time t1, what is the magnetic field B1 at a radius r
(point d) in between the plates of the capacitor?
●d I1 r
R Q1 • Conceptual and Strategic Analysis
• Charge Q1 creates electric field between the plates of C
• Charge Q1 changing in time gives rise to a changing electric flux between
the plates
• Changing electric flux gives rise to a displacement current ID in between
the plates
• Apply (modified) Ampere’s law using ID to determine B
10 Physics 212 Lecture 21, Slide 7 Calculation
S Switch S has been open a long time when at t = 0, it is closed.
Capacitor C has circular plates of radius R. At time t = t1, a
V
current I1 flows in the circuit and the capacitor carries
charge Q1.
c● ●d r
I1 C
Ra r
R Q1 BB Compare the magnitudes of the B fields at points c and d. (A) Bc < Bd (B) Bc = Bd
What is the difference?
Apply (modified) Ampere’s Law point c:
I(enclosed) = I1
11 r
X (C) Bc > Bd r R point d:
ID(enclosed) < I1
Physics 212 Lecture 21, Slide 8 Calculation
Switch S has been open a long time when at t = 0, it is closed.
Capacitor C has circular plates of radius R. At time t = t1, a
V
current I1 flows in the circuit and the capacitor carries
charge Q1.
●d I1 E S
C
Ra r σ R E=ε
0 Q1 BB What is the magnitude of the electric field between the plates?
Q
Q1
Q
Q1π R 2
(A) E =
(B) E =
(C) E = 1
(D) E = 1
ε0
π R 2ε 0
r
ε0 Q1 13 E=
R σ
ε0 σ= Q1
Q
= 12
A πR E= Q1
ε 0π R 2 Physics 212 Lecture 21, Slide 9 Calculation
S Switch S has been open a long time when at t = 0, it is closed.
Capacitor C has circular plates of radius R. At time t = t1, a
V
current I1 flows in the circuit and the capacitor carries
charge Q1.
●d I1 E C
Ra E=
r Q1
π R 2ε 0 R Q1 BB What is the electric flux through a circle of radius r in between the plates?
Q1
Q1 2
Q1π r 2
Q1r 2
2
(A) Φ E = π r
(B) Φ E = π R
(C) Φ E =
(D) Φ E =
2
ε0
ε0
ε 0R2
ε0R r 15 R rr
ΦE = E ⋅ A Q1
E =
π r2
ε 0π R 2 Q1 r 2
ΦE =
ε 0 R2
Physics 212 Lecture 21, Slide 10
10 Calculation
S Switch S has been open a long time when at t = 0, it is closed.
Capacitor C has circular plates of radius R. At time t = t1, a
V
current I1 flows in the circuit and the capacitor carries
charge Q1.
●d I1 E
Q1 Ra
Q1r 2
ΦE =
ε 0R2 r
R C dΦE
ID = ε0
dt BB What is the displacement current enclosed by circle of radius r ? R2
(A) I D = I1 2
r r 17 r
(B) I D = I1
R R r2
(C) I D = I1 2
R (D) I D = I1 R
r d ΦE dQ1 r 2
r2
ID = ε0
=
= I1 2
2
dt R
dt
R
r2
I D = I1 2
R
Physics 212 Lecture 21, Slide 11
11 Calculation
S Switch S has been open a long time when at t = 0, it is closed.
Capacitor C has circular plates of radius R. At time t = t1, a
V
current I1 flows in the circuit and the capacitor carries
charge Q1.
●d I1 E Ra r2
I D = I1 2
R r
R C rr
∫ B ⋅ d l = µ o (I + I D ) Q1 BB What is the magnitude of the B field at radius r ? (A) B = µ0 I1
2π R r 19 µ0 I1
2π r µI R
(C) B = 0 1 2
2π r
rr
Ampere’s Law: ∫ B ⋅ d l = µo (I + I D ) (B) B = R (D) B = r2 B ⋅ 2π r = µ0 0 + I1 2 R µ0 I1 r
B=
Physics 212
2π R 2 µ0 I1 r
2π R 2 Lecture 21, Slide 12
12 Preflight 4
Preflight
BB A
B
C
From the
From
calculation we
just did:
just µ0 I1 r
B=
2π R 2
21 70 30 60
50
40 20
10
0 Physics 212 Lecture 21, Slide 13
13 Preflight 2
Preflight
BB
BB B= µ0 I1 r
2π R 2 B is proportional to I
but
At A, B = 0 !! 80
60
40
20
0 Physics 212 Lecture 21, Slide 14
14 FollowUp
Switch S has been open a long time when at t = 0, it is
closed. Capacitor C has circular plates of radius R. At
time t = t1, a current I1 flows in the circuit and the
capacitor carries charge Q1.
What is the time dependence of the magnetic field B
at a radius r between the plates of the capacitor? (A) (B) S
C BB V
Ra B1 = µ0 I1 r
2π R 2 (C) B at fixed r is proportional to the current I
Close switch: VC =0 ﬂ I = V/Ra (maximum)
I exponentially decays with time constant τ = RaC
25 Physics 212 Lecture 21, Slide 15
15 FollowUp 2
Suppose you were able to charge a capacitor with
constant current (does not change in time).
Does a B field exist in between the plates of the
capacitor? (A) YES (B) BB NO Constant current ﬂ Q increases linearly with time
Therefore E increases linearly with time ( E = Q/(Aε0)
dE/dt is not zero ﬂ Displacement current is not zero
ﬂ B is not zero !
Physics 212 Lecture 21, Slide 16
16 We learned about waves in Physics 211 30 Physics 212 Lecture 21, Slide 17
17 “How can light move at
How
the same velocity in
any inertial frame of
reference? That's
really trippy. ”
really
see PHYS 225
see PHYS
33 Physics 212 Lecture 21, Slide 18
18 35 Physics 212 Lecture 21, Slide 19
19 37 Physics 212 Lecture 21, Slide 20
20 Preflight 6
Ex = E0sin(kzωt) BB 50
40 E = E0 sin (kz  ωt):
t):
E depends only on z coordinate for constant t.
z coordinate is same for A, B, C.
coordinate 30
20
10
0 40 Physics 212 Lecture 21, Slide 21
21 Preflight 7
Ex = E0sin(kzωt) 60
50 E = E0 sin (kz  ωt):
t):
E depends only on z coordinate for constant t.
z coordinate is same for A, B, C.
coordinate 40
30
20
10
0 45 Physics 212 Lecture 21, Slide 22
22 ACT
Ex = E0sin(kzωt) Consider a point (x,y,z) at time t when Ex
is negative and has its maximum value.
At (x,y,z) at time t, what is By?
A)
B)
C)
D) 45 By is positive and has its maximum value
By is negative and has its maximum value
By is zero
We do not have enough information
We Physics 212 Lecture 21, Slide 23
23 ...
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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
 Physics

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