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NOTES Maxwell’S Equations ( Incomplete So Far) NOTES Maxwell’s Equations ( incomplete so far) Gauss’s law Gauss’ law for magnetism Faraday’s law Ampere’s law Parallel-Plate Capacitor Revisited For surface S , I = I, B=0 ? Not -Q 1 s experimentally! but for surface S2, Is = 0 Q Wait, LHS is the same (because C is the same)! ?? You could make this work if a fictitious current Id is added to Is in such a way that Id is zero for S1 but is equal to I for S2. will work. Displacement Current James Clerk Maxwell proposed that a changing electric field induces a magnetic field, in analogy to Faraday’s law: where a changing magnetic field induces an electric field. Ampere’s law is revised to become Ampere-Maxwell law where is the displacement current. MAXWELL’S EQUATIONS “COMPLETED” Basis for Electromagnetic Waves! The equations are often written in slightly different (and more convenient) forms when dielectric and/or magnetic materials are present. MAXWELLS EQUATIONS James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish theoretical physicist] His most prominent achievement was formulating a set of equations that united previously unrelated observations, experiments, and equations of electricity, magnetism, and optics into a consistent theory. His theory of classical electromagnetism demonstrates that electricity, magnetism and light are all manifestations of the same phenomenon, namely the electromagnetic field. Maxwell's achievements concerning electromagnetism have been called the "second great unification in physics” after the first one realized by Isaac Newton. Maxwell demonstrated that electric and magnetic fields travel through space in the form of waves at the speed of light in 1865, with the publication of A Dynamical Theory of the Electromagnetic Field. Maxwell proposed that light was in fact undulations in the same medium that is the cause of electric and magnetic phenomena. The unification of light and electrical phenomena led to the prediction of the existence of radio waves. TRANSVERSE ELECTROMAGNET WAVE T E M wave NOTES 7B-20 TRANSVERSE ELECTROMAGNETIC WAVE Notation for a TEM wave traveling in the + x direction ( Change + to – for traveling in the – x drection ) Ey = Em sin 2π ( x/λ - t/T ) T=1/f, ω = 2πf Bz = Bm sin 2π ( x/λ – t/T ) k = 2π/λ 2π/λ measures x the longitudinal extension 2π/T = 2πf measures t the time ELECTOMAGNETIC WAVE FARADAY INDUCTION PART Electromagnetic Waves From Faraday’s Law c TRANSVERSE ELECTROMAGNETIC WAVE AMPERE LAW PART Electromagnetic Waves From Ampère’s Law Electric Dipole Radiation Electromagnetic Wave Propagation in Free Space So, again we have a traveling electromagnetic wave speed of light in vacuum Ampere’s Law Faraday’s Law Speed of light in vacuum is currently defined rather than measured (thus defining meter and Wave Equation also the vacuum permittivity). NOTES Plane Electromagnetic Waves where c • Transverse wave • Plane wave (points of given phase form a plane) x • Linearly polarized (fixed plane contains E) 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 • So Total energy density is Energy Propagation in Electromagnetic Waves Energy flux density equals Energy transmitted through unit time per unit area • Intensity I = Average energy flux density (W/m2) Define Poynting vector Direction is that of wave propagation average magnitude is the intensity 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 Δt , the energy flux through area A is ΔU =IA Δ t . If radiation is totally absorbed: momentum imparted radiation pressure EXERTED If radiation is totally reflected: x2 Maxwell’s Rainbow Light is an Electromagnetic Wave NOTES Physics 241 - Extra QUIZ 3 An electromagnetic wave is traveling in +x direction and the electric field at a particular point on the x-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the magnetic field? a) -z z b) -x E c) -y y d) +y e) None of the above x The direction of travel is that of E x B. Physics 241 – Extra QUIZ 3 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 the +y direction at a certain instant in time. Which direction is this wave traveling? z a) +x E b) -x y c) -y B d) -z x The direction of travel e) None of the above is that of E x B. .
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