Download Lecture 14.1 : Electromagnetic Fields

Lecture 14.1 :
Electromagnetic Fields
Lecture Outline:
E & B Transformations
The Displacement Current
Textbook Reading:
Ch. 34.1 - 34.3
April 16, 2013
1
Announcements
•Homework #11 due on Monday, April 22, at 9pm.
•Quiz #5 on Thursday will cover Ch. 33 material (33.1-33.9).
•Online Evaluation e-mails will be sent to you on Monday, April 22.
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May 8 is
deadline.
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‣Remember that PHY212 and PHY222 (lab) are separate courses!
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Last Lecture...
Maxwell proposed that a changing electric field induces a
magnetic field (mirror idea to Faraday’s law, which says
changing magnetic field induces an electric field).
3
Last Lecture...
Inductors are devices in circuits that can be used to store
energy in magnetic fields (similar to Capacitors storing
energy in electric fields). They have interesting behavior
when placed in circuits.
Inductance
Φm
L≡
I
1 henry = 1 H ≡ 1 Wb/A = 1 Tm2 /A
4
Last Lecture...
If the current through an inductor is changing, a potential
difference develops across the inductor.
Induced current
Induced field
�
�
� �
� dΦm �
� dI �
� = L� �
∆VL = ��
� dt �
dt �
We choose same sign convention as
in resistors...voltage decreases in
direction of current flow.
5
Last Lecture...
We worked out the potential energy stored in the magnetic field
of an inductor:
1
2
UL =
A·�·B
2µ0
We could convert this to an energy density by dividing out the
volume of the inductor. This result is actually very general.
1 2
uB =
B
2µ0
Recall for Electric Fields:
1
uE = � 0 E 2
2
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The Can Crusher Demo
5K20.65
Eddy Currents
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Clicker Question #1
Sharon runs past Bill while
holding a positive charge q.
In Bill’s reference frame,
there is (or are)
A.
B.
C.
D.
Only an electric field.
Only a magnetic field.
An electric and a magnetic field.
No fields.
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Clicker Question #2
Sharon runs past Bill while
holding a positive charge q.
In Sharon’s reference frame,
there is (or are)
A.
B.
C.
D.
Only an electric field.
Only a magnetic field.
An electric and a magnetic field.
No fields.
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E & B Transformations
Our current understanding of electric and magnetic
fields can lead to some confusing scenarios:
•As Brittney runs by Alec, he sees a moving charge and hence
a magnetic field, while Brittney doesn’t see any magnetic field.
•If Alec creates a magnetic field that Brittney runs through, he
expects a magnetic force on the charge, while she does not.
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E & B Transformations
Recall that inertial reference frames move at constant
velocity with respect to one another. Newton’s laws are
valid in inertial frames.
�vCA = �vCB + �vBA
d�vCA
d�vCB
d�vBA
=
+
dt
dt
dt
�aCA = �aCB
Observers in either frame agree on the acceleration of particle C,
so they agree on the net force acting on the particle.
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E & B Transformations
Alec creates a region with zero electric field, and magnetic field
BA. He observes a particle with velocity vCA traveling through
this region to experience force FA.
Brittney runs alongside the charge. What does she observe?
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E & B Transformations
Alec creates a region with zero electric field, and magnetic field
BA. He observes a particle with velocity vCA traveling through
this region to experience force FA.
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E & B Transformations
More generally, a charge can move through E and B fields with velocity vCA .
We can imagine an observer moving at the same velocity as the charge.
�B = E
� A + �vCA × B
�A
E
Note: Frame B still can’t say anything about possible magnetic fields since
they are at rest with respect to the charge.
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E & B Transformations
What about transforming magnetic fields between frames?
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Clicker Question #3
Experimenters on earth have
created the magnetic field
shown. A rocket flies through
the field, from right to left.
Which are the field (or fields)
in the rocket’s reference frame?
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E & B Transformations
A warning about “relativity” and Einstein...
Fields at q2 due to q1:
1
q
1
�
EA =
ĵ
4π�0 r2
µ0 q1 vCA
�
BA =
k̂
2
4π r
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Clicker Question #4
The E & B fields in frame A are shown. Which diagram
shows the fields in frame B?
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The Displacement Current
Recall Ampere’s Law:
�
� · d�s = µ0 Ithrough
B
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The Displacement Current
No rule saying we have to pick surface S1. We could
also choose to evaluate Ampere’s Law through S2,
which is bounded by the same curve.
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The Displacement Current
Consider the circuit below with a capacitor and a
battery. It appears we will get very different values for
Ithrough depending on which surface we use.
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The Displacement Current
We need to modify Ampere’s Law to account for
what’s happening in surface S2. This surface sees a
changing electric flux.
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Reminders
•Read Ch. 34.
•Quiz #5 on Thursday.
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