lecture 14.2 : maxwell’s equations · lecture outline:! the displacement current! maxwell’s...
TRANSCRIPT
1
Lecture 14.2 :!Maxwell’s Equations
Lecture Outline:!The Displacement Current!
Maxwell’s Equations!Electromagnetic Waves!
April 17, 2014
Textbook Reading:!Ch. 34.3 - 34.5
Announcements
2
!
•Homework #11 due on Tuesday, April 22, at 9am.!
•Quiz #6 next Thursday, April 24. (~Ch. 33.7-34.5)!
•If you’ve been using your clicker some/all of the semester, make sure it is registered (via Blackboard->Tools->Turning Technologies Registration Tool). By the end of next week, I will post your Clicker extra-credit point total for the semester…I will not adjust these once final course grades have been submitted. !
!
Last Lecture...
3
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.
�EB = �EA + �vCA � �BA
Note: Frame B still can’t say anything about possible magnetic fields since they are at rest with respect to the charge.
Last Lecture...
4
General equations for transforming electric and magnetic fields between two inertial reference frames:
E & B Transformations
5
Example: Scientists in the laboratory create a uniform electric field E = 1.0x106 V/m in the positive z-direction in a region of space
where B = 0 T. What are the E and B fields in the reference frame of a rocket traveling in the positive x-direction at 1.0x106 m/s?
The Displacement Current
6
��B · d�s = µ0Ithrough
Recall Ampere’s Law:
The Displacement Current
7
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.
The Displacement Current
8
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.
⇤⇥B · d⇥s = µ0
�Ithrough + �0
d�e
dt
⇥
The Displacement Current
9
⇤⇥B · d⇥s = µ0
�Ithrough + �0
d�e
dt
⇥
��E · d�s = �d�m
dt
Maxwell’s Equations
10
James Clerk Maxwell!1831-1879
Electromagnetic Waves
11
“Source-free” Maxwell’s equations (no charge or current)
�⇥E · d ⇥A = 0
�⇥E · d⇥s = �d�m
dt�⇥B · d ⇥A = 0
�⇥B · d⇥s = �0µ0
d�e
dt
Electromagnetic Waves
12
Ey = E0sin (2⇥(x/�� ft))
Bz = B0sin (2⇥(x/�� ft))
Bx = By = 0
Ex = Ez = 0
Electromagnetic Waves
13
Electromagnetic Waves
14
�Ey
�x= ��Bz
�t
E0 = vemB0
Condition on EM Waves from Faraday’s Law
Electromagnetic Waves
15
⇥Bz
⇥x= ��0µ0
⇥Ey
⇥tCondition on EM Waves
from Ampere-Maxwell Law
Electromagnetic Waves
16
1
�0µ0vem= vem
E0 =B0
�0µ0vemE0 = vemB0
Electromagnetic Waves must travel at the Speed of Light!
vem wave =1
⇤�0µ0
⇥ 3.0� 108m/s = c
We now have two relations on E0 and B0 that both need to be true.
“The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws”
- Maxwell
Electromagnetic Waves
17
The Electromagnetic Spectrum
Reminders
18
!
•Read Ch. 34.!•Quiz #6 on Thursday next week.