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Physics 2112 Unit 22 Outline Displacement Current Maxwell’s Equations (Final Form) E&M Waves Electricity & Magnetism Lecture 22, Slide 1

Physics 2112 Unit 22

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Physics 2112 Unit 22. Outline Displacement Current Maxwell’s Equations (Final Form) E&M Waves. Where we are now. Faraday’s Law. Gauss’ Law. Ampere’s Law. Gauss’ Law for B field. Our equations so far…. Displacement Current. - PowerPoint PPT Presentation

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Page 1: Physics 2112 Unit 22

Physics 2112Unit 22

Outline Displacement Current Maxwell’s Equations (Final Form) E&M Waves

Electricity & Magnetism Lecture 22, Slide 1

Page 2: Physics 2112 Unit 22

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

Page 3: Physics 2112 Unit 22

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:

Page 4: Physics 2112 Unit 22

Modify Ampere’s Law

Electricity & Magnetism Lecture 22, Slide 4

A

QE

00

0Q

EA

0Q

DIdt

d

td

dQ

0

Page 5: Physics 2112 Unit 22

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

Page 6: Physics 2112 Unit 22

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?

Page 7: Physics 2112 Unit 22

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

Page 8: Physics 2112 Unit 22

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

Page 9: Physics 2112 Unit 22

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

Page 10: Physics 2112 Unit 22

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

Page 11: Physics 2112 Unit 22

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

Page 12: Physics 2112 Unit 22

Wave Equation

Electricity & Magnetism Lecture 22, Slide 12

Remember this guy? Not the spring

constant!

Remember from 2111??

Page 13: Physics 2112 Unit 22

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

Page 14: Physics 2112 Unit 22

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

Page 15: Physics 2112 Unit 22

Electricity & Magnetism Lecture 22, Slide 15

Only true for

E&M wave

traveling in

space

Page 16: Physics 2112 Unit 22

Electricity & Magnetism Lecture 22, Slide 16

The Sun

Keep us warm

Keep us safe

Page 17: Physics 2112 Unit 22

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?

Page 18: Physics 2112 Unit 22

Electricity & Magnetism Lecture 22, Slide 18

Past Confusion

Nothing is moving here.

Arrows only represent strength of field.

Actually a plane wave.

Page 19: Physics 2112 Unit 22

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

Page 20: Physics 2112 Unit 22

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