Electromagnetic Radiation Flashcards
Wave - Particle Duality
- when dealing with its propagation, light is best described by waves
- when dealing with energy, light is best described as particles
Faraday’s Law
induced EMF = - rate of change of magnetic flux through circuit
∂E/∂x = - ∂B/∂t
Electrostatic Force
^F = k q1q2/r (^r12) = q^E
Magnetic Force
^F = q^v x ^B
Maxwell’s Formulation of Faraday’s Law
dE/dB = dx/dt
Maxwell’s Formulation of Ampere’s Law
∂B/∂x = μ0 ε0 ∂E/∂t
Perpendicular E and B Fields and the Wave Equation
-for perpendicular E and B fields starting from Maxwell’s formulation of Ampere’s Law and Faraday’s Law respectively it is possible to show that both B and E obey the wave equation
Wave Speed
-Maxwell’s equations give a wave speed
v = 1/√(μ0 ε0) = c
-Maxwell had discovered the electromagnetic wave nature of light
Electromagnetic Waves
- Maxwell found that electromagnetic waves should exist
- oscillating electric and magnetic fields perpendicular to each other and the direction of propagation
Harmonic Travelling Wave Solutions of the Wave Equation
B = B0 cos(kx-t)
E = E0 cos((kx-ωt)
Travelling Waves Velocity Equation
v = ω/k
Electromagnetic Waves - Field Amplitudes Equation
E0 = cB0
and since the waves are in phase
E = cB
The Del Operator, ∇
∇ = ∂/∂x i + ∂/∂y j + ∂/∂z k
∇f
gradient of a scalar function is a vector quantity
∇.A
divergence of a vector is a scalar quantity
∇xA
curl of a vector is a vector quantity
∇²A
the Lalacian of a scalar A
The Propagation of Light - Huygen’s Principle
- all points on a wavefront are taken as point sources for the production of spherical secondary waves called wavelets
- wavelets propagate outwards at the characteristic speed of waves in that medium
- after some time has elapsed, the new position of the wavefront is the surface tangent to the wavelets
Interference
Definition
-the combining by superposition of two or more waves of the same frequency
Diffraction
Definition
- the phenomenon whereby an aperture behaves like a source
- it causes waves to travel around corners, when a portion of a wave-front is cut off by a barrier
Intensity and Amplitude
I ∝ A²
