Lecture physics a2 electromagnetic fields and waves

ELECTROMAGNETIC FIELDS AND WAVES Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 CONTENTS Maxwell’s Equations Displacement current Plane Electromagnetic Waves – Wave equation Energy Carr[.]

ELECTROMAGNETIC

FIELDS AND WAVES

Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016

CONTENTS

- Maxwell’s Equations

- Displacement current

- Plane Electromagnetic Waves – Wave equation

- Energy Carried by Electromagnetic Waves, Poynting vector

Waves

• Maxwell discovered that the basic principles of

ectromagnetism can be expressed in terms of the four

equations that we now call Maxwell’s equations

• These four equations are

(1) Faraday’s law,

(2) Ampere’s law, including displacement current;

(3) Gauss’s law for electric fields;

(4) Gauss’s law for magnetic fields, showing the absence of

magnetic monopoles

Review : Gauss’s Law for electric field

The flux of the electric field (the area integral of the electric field) over any closed surface (S) is equal to the net charge inside the surface (S) divided by the permittivity o

0

in

S surface closed E

q S

d

E









Review : Gauss’s law of magnetism

Gauss’s law of magnetism states that the net

magnetic flux through any closed surface is zero:

0 S

d

B

S



  

The magnetic field lines are closed lines

The number of magnetic field lines that exit equal The number of magnetic field lines that enter the closed surface

S

d 

B 

(S)

path closed

the by bounded

surface _

through going

i o

) C (

I d

.

B   



















) C

(

o )

C (

o )

C

(

o z

r o

z r

d 2

I d

2

I d

.

B

d 2

I )

e dz

e rd

e dr

.(

e r

2

I d

.

B

e dz

e rd

e

dr

d

r 2

































































r 2

I

B o







I

path closed

the by

bounded

surfaced any

through current

total the

is I where

I, μ

equals path

closed any

around

.d B of integral line

the that

says law

s Ampere'

o





 d

B 

r +

0 I

or 0 I

that

integral line

the of

direction the

to relative

current the

of direction the

on depends it

i



i

i (C)

I d

H 

Magnetic filed B is sometimes called magnetic induction,

(vector cảm ứng từ)

Magnetic field H , magnetic field strength , (cường độ từ

trường)

H

B  o r 







Review: Faraday’s law of induction

when the magnetic flux through the loop changes with time, there is an emf induced in a loop













S

dt

d dt









) S (

B B  d S 

is the magnetic flux through the loop where

B E

rot dS

.

B dt

d d

.

E

S











) t (

B 

(C)

Maxwell - Faraday’s equation states that a time varying

magnetic field induces an electric field

Maxwell -Faraday’s equation states that the emf, which is the line integral of the electric field around any closed path,

equals the rate of change of magnetic flux through any

surface bounded by that path

1 Time-changing electric fields induces magnetic fields

2 Displacement current

Conduction currents

( motion of charged particles) cause Magnetic field

Time changing electric fields also cause Magnetic field

=> Time changing electric fields is equivalent to a current We call it

dispalcement current

3 Displacement current density

E D

t

E t

D j

r o

r o d



























 Electric field E, vector cường độ điện trường

Electric Displacement field D : vector cảm ứng điện

D j

H rot dS

t

D j

d H

S











































 







S

d t

displcemen conduction

I

current

nt displaceme and

current conduction

of sum the

to equal is

current total

The

path.

closed

by the bounded

surface any

through going

current total

the

to equal is

(C) path closed

a over H

vector of

integral

“Line







