Lecture 21 1 Maxwells Equations so far Gausss

Lecture 21 -1 Maxwell’s Equations (so far) Gauss’s law Gauss’ law for magnetism Faraday’s law Ampere’s law*

Lecture 21 -2 Parallel-Plate Capacitor Revisited -Q Q will work.

Lecture 21 -3 Displacement Current James Clerk Maxwell proposed that a changing electric field induces a magnetic field, in analogy to Faraday’s law: A changing magnetic field induces an electric field. Ampere’s law is revised to become Ampere-Maxwell law where is the displacement current.

Lecture 21 -4 Maxwell’s Equations Basis for electromagnetic waves!

Lecture 21 -5 Electromagnetic Waves From Faraday’s Law

Lecture 21 -6 Electromagnetic Waves From Faraday’s Law c Direction of propagation is always the direction of

Lecture 21 -7 Electromagnetic Waves From Ampère’s Law Empty space (I=0) Direction of propagation is always the direction of

Lecture 21 -8 Electromagnetic Wave Propagation in Free Space So, again we have a traveling electromagnetic wave speed of light in vacuum Ampere’s Law Speed of light in vacuum is currently defined rather than measured (thus defining meter and also the vacuum permittivity). Faraday’s Law Wave Equation where

Lecture 21 -9 Quiz Question 1 Electromagnetic wave travel in space where E is electric field, B is magnetic field. Which of the following diagram is true? z (a). z (b). E x y travel direction B x E y B z travel direction (c). E x B z (d). y E travel direction x B y

Lecture 21 -10 Energy Density of Electromagnetic Waves • Electromagnetic waves contain energy. We know already expressions for the energy density stored in E and B fields: EM wave remember • So Total energy density is

Lecture 21 -11 Energy Propagation in Electromagnetic Waves • Energy flux density = Energy transmitted through unit time per unit area • Intensity I = Average energy flux density (W/m 2) Define Poynting vector Ø Direction is that of wave propagation Ø average magnitude is the intensity

Lecture 21 -12 Radiation Pressure Electromagnetic waves carry momentum as well as energy. In terms of total energy of a wave U, the momentum is U/c. During a time interval t , the energy flux through area A is U =IA t. Ø If radiation is totally absorbed: momentum imparted radiation pressure EXERTED Ø If radiation is totally reflected:

Lecture 21 -13 Maxwell’s Rainbow Light is an Electromagnetic Wave

Lecture 21 -14 Quiz Question 2 An electromagnetic wave is traveling through a particular point in space where the direction of the electric field is along the +z direction and that of the magnetic field is along +y direction at a certain instant in time. Which direction is this wave traveling in? a) +x b) x c) y d) z e) None of the above

Lecture 21 -15 Quiz Question 3 An electromagnetic wave is traveling in +y direction and the magnetic field at a particular point on the y-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the electric field? a) z b) x c) y d) +x e) None of the above