Class Notes (1,100,000)

US (460,000)

UC-Irvine (10,000)

PHYSICS (500)

PHYSICS 7E (70)

GUERRA, A (10)

Lecture 12

# PHYSICS 7E Lecture Notes - Lecture 12: Partial Differential Equation, Electric Flux, Electric FieldPremium

by OC1211656

Department

PhysicsCourse Code

PHYSICS 7EProfessor

GUERRA, ALecture

12This

**preview**shows half of the first page. to view the full**3 pages of the document.**11/05/19

PHYSICS 7E - Lecture 12 - Electromagnetic Waves

Electromagnetic Waves

●Electromagnetic (em) waves permeate our environment

●EM waves can propagate through a vacuum

●Much of the behavior of mechanical wave models is similar for em waves

●Maxwell’s equations form the basis of all electromagnetic phenomena

Maxwell’s Equation

●In his unified theory of electromagnetism, Maxwell showed that electromagnetic waves

are a natural consequence of the fundamental laws expressed in these four equations:

○Gauss’ Law (electric flux)

○Gauss’ Law for magnetism

○Faraday’s Law of induction

○Ampere’s Law, General form

∮AE ·d=q

ε0

∮AB ·d= 0

sE ·d= − dt

dΘB∮s l εB·d= μ0+ μ0 0 dt

dΘE

▽·E=ρ

ε0

▽·B= 0

▽×E= − ∂t

∂B

ε ▽J×B= μ0+ μ0 0 ∂t

∂E

Derivation of Speed of EM Wave

●From Maxwell’s equations applied to empty space, the following partial derivatives can

be found:

○ε

∂x2

∂E

2= μoo∂t2

∂E

2

and ε

∂x2

∂B

2= μoo∂t2

∂B

2

●The simplest solution to the partial differential equations is a sinusoidal wave:

○cos(kx t)E=Emax − ω /v=c= 1 √μ ε

oo

○cos(kx t)B=Bmax − ω

●These are in the form of a general wave equation, with

●Substituting the values for and gives m/sμoεo.99792 10c= 2 × 8

E, B, and C

●The speed of the electromagnetic wave is

○f

k

ω=2πf

2π/λ = λ = c

●Taking partial derivatives also gives

###### You're Reading a Preview

Unlock to view full version

Subscribers Only