Physics 212 Lecture 21, Slide 1

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Physics 212 Lecture 21
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Some of your comments
More cowbell please.
These equations just keep getting more and more
confusing. It would be helpful if they were
explained more as far as how to use them.
deriving the displacement current and the
relationship between electric and magnetic
fields.2.
Everything. You said this would get easier but
this might be the hardest one yet. I don't get
it..
too much work for credit hours given in this
class, seriously needs to be looked into
Explain, in-depth, Einstein's theory of
relativity in 2 minutes. Go.
Is this for real? Like I opened the prelecture
and just went "Ah buhuh?" Please make this
simple. And if you could make TAM212 simple I'd
like that too
how can the speed of light be the same in any
inertial reference frame? what if you're going
the speed of light? shouldn't the speed of light
be 0 in that reference frame? this is some crazy
sht man.
I liked the old Ampere's Law, WHY DID YOU HAVE TO
CHANGE IT!!!!!!!!!!!
This prelecture was fascinating! Please just go
over it all again. It's so awesome that electric
fields are so intrinsically related to magnetic
fields. Considering changing my major? Very much
so.
For the derivation part, why did we use fardays
law for Dx and ampere's law for Dy. I mean,
wasn't that just a lucky guess that magnetism
movies in the y-direction? Maybe I missed
something, but it seems like that one was just
swept under the carpet. Also, this EM wave stuff
is kind of blowing my mind. Can we, like, chill
on this for a few days so i can wrap my head
around it? Gracias, gue.
steve nash is canadian, like mats! could you
invite him to class?
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But so far we have ignored dQ/dt in the capacitor
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Displacement Current
Real Current Charge Q passes
through area A in time t Displacement Current
Electric flux through area A changes in time
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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 current I1 flows in
the circuit and the capacitor carries charge
Q1. At time t1, what is the magnetic field B1 at
a radius r (point d) in between the plates of the
capacitor?
?
d
r
I1
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) Amperes law using ID to
  determine B

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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 current I1 flows in
the circuit and the capacitor carries charge Q1.
?
c
?
d
r
r
I1
R
Q1
What is the difference? Apply (modified)
Amperes Law
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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 current I1 flows in
the circuit and the capacitor carries charge Q1.
?
d
r
I1
E
R
Q1
What is the magnitude of the electric field
between the plates?
(A) (B)
(C) (D)
Q1
R
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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 current I1 flows in
the circuit and the capacitor carries charge Q1.
?
d
r
I1
E
R
Q1
What is the electric flux through a circle of
radius r in between the plates?
(A) (B)
(C) (D)
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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 current I1 flows in
the circuit and the capacitor carries charge Q1.
?
d
r
I1
E
R
Q1
What is the displacement current enclosed by
circle of radius r ?
(A) (B)
(C) (D)
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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 current I1 flows in
the circuit and the capacitor carries charge Q1.
?
d
r
I1
E
R
Q1
What is the magnitude of the B field at radius r
?
(A) (B)
(C) (D)
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Preflight
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Preflight
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Follow-Up
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?
B at fixed r is proportional to the current
I Close switch VC 0 ? I V/Ra (maximum) I
exponentially decays with time constant t RaC
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We learned about waves in Physics 211
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Preflight
Ex E0sin(kz-wt)
E A sin (kz - wt) E depends only on z
coordinate for constant t. z coordinate is same
for A, B, C.
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Preflight
Ex E0sin(kz-wt)
All three are at the same distance Z so the
fields are all equal.
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