Physics 2112 Unit 22
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Transcript of Physics 2112 Unit 22
Physics 2112Unit 22
Outline Displacement Current Maxwell’s Equations (Final Form) E&M Waves
Electricity & Magnetism Lecture 22, Slide 1
Where we are now
surface
AdB 0
ENCLo
loop
IldB
AdBdt
dldE
loop
o
enc
surface
QAdE
Our equations so far…..
Unit 22, Slide 2
Gauss’ Law
Gauss’ Law for B fieldAmpere’s Law
Faraday’s Law
3 Points, all a distance r from axis of a current c carrying wire connected to capacitor
Displacement Current
Electricity & Magnetism Lecture 22, Slide 3
●r
●
I1
1 3●
2
rIBB o 2/|||| 31
??0|| 2 B
)( disENCLo
loop
IIldB Define
“displacement current” such that:
Modify Ampere’s Law
Electricity & Magnetism Lecture 22, Slide 4
A
QE
00
0Q
EA
0Q
DIdt
d
td
dQ
0
Real Current: Charge Q passes through area A in time t:
Displacement Current: Electric flux through area A changes in time
Displacement Current
Electricity & Magnetism Lecture 22, Slide 5
dt
dI E
D
0
td
dQI
)(dt
dIldB E
oENCLo
loop
A parrallel plate capacitor has plates that are 2cm in diameter and 1mm apart. If the current into the capacitor is 0.5A, what is the magnetic field between the plates 0.5cm from the axis of the center of the plates?
R
r●
I1
Q1
d
Conceptual PlanUse modified Ampere’s Law
Strategic PlanFind electric flux contained within circle with radius of 0.5cmFind time rate of change of that flux
Example 22.1
Electricity & Magnetism Lecture 22, Slide 6
1cm
0.5cm
What is the magnetic field 3cm from the axis of the center of the plates?
CheckPoint 1(A)
Electricity & Magnetism Lecture 22, Slide 7
At time t = 0 the switch in the circuit shown below is closed. Points A and B lie inside the capacitor; A is at the center and B is at the outer edge..
A
After the switch is closed, there will be a magnetic field at point A which is proportional to the current in the circuit.
A. True B. False
CheckPoint 1(B)
Electricity & Magnetism Lecture 22, Slide 8
At time t = 0 the switch in the circuit shown below is closed. Points A and B lie inside the capacitor; A is at the center and B is at the outer edge..
A
Compare the magnitudes of the magnetic fields at points A and B just after the switch is closed:
A. BA < BB B. BA = BB C. BA > BB
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?
0 11 22
I rB
R
(A) (B) (C)
Follow-Up
Electricity & Magnetism Lecture 22, Slide 9
S
Ra
V C
A B C
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) NO
Follow-Up 2
Electricity & Magnetism Lecture 22, Slide 10
Final form
surface
AdB 0
AdEdt
dIldB oENCLo
loop
AdBdt
dldE
loop
o
enc
surface
QAdE
Tada!..... Maxwell’s Equations
Unit 22, Slide 11
Gauss’ Law
Gauss’ Law for B fieldAmpere’s Law
Faraday’s Law
Wave Equation
Electricity & Magnetism Lecture 22, Slide 12
Remember this guy? Not the spring
constant!
Remember from 2111??
Electricity & Magnetism Lecture 22, Slide 13
++
--
AdBdt
dldE
loop
Bhdxdt
dhEd )*(*
dx
Bd
dt
d
dx
Ed
2
2
AdEdt
dldB oo
loop
dt
Ed
dx
Bdoo
Some Calculations
see PHYS 2115
Electricity & Magnetism Lecture 22, Slide 14
2
2
2
2
dx
Ed
dx
Edoo
A wave equation????
oo
v
1
With a velocity of …?
Some Calculations
Electricity & Magnetism Lecture 22, Slide 15
Only true for
E&M wave
traveling in
space
Electricity & Magnetism Lecture 22, Slide 16
The Sun
Keep us warm
Keep us safe
Electricity & Magnetism Lecture 22, Slide 17
Example 22.2
An electromagnetic plane wave has a wavelength of 0.100nm.
a) What is its wave number, k?b) What is its frequency?c) What portion of the electro-magnetic spectrum
does it fall in?
Electricity & Magnetism Lecture 22, Slide 18
Past Confusion
Nothing is moving here.
Arrows only represent strength of field.
Actually a plane wave.
CheckPoint 2(A)
Electricity & Magnetism Lecture 22, Slide 19
Ex = E0sin(kz - wt)
E = E0 sin (kz - wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C.
An electromagnetic plane wave is traveling in the +z direction. The illustration below shows this wave an some instant in time. Points A, B, and C have the same z coordinate.
Compare the magnitudes of the electric field at points A and B. A. Ea < Eb B. Ea = Eb C. Ea > Eb
CheckPoint 2(B)
Electricity & Magnetism Lecture 22, Slide 20
Ex = E0sin(kz - wt)
E = E0 sin (kz - wt): E depends only on z coordinate for constant t. z coordinate is same for A, B, C.
An electromagnetic plane wave is traveling in the +z direction. The illustration below shows this wave an some instant in time. Points A, B, and C have the same z coordinate.
Compare the magnitudes of the electric field at points A and C. A. Ea < Ec B. Ea = Ec C. Ea > Ec