Notes on Light (electromagnetic) Waves MJM March 28 01

• Electric field induced by changing magnetic flux.
• When the magnetic flux changes it induces an emf (this is Faraday's law, Ch 30)
• This induced emf equals the line integral of E dot dl around a curve C (Section 30.2)
• The E is an induced electric field (induced because the magnetic flux changed with time)

• Magnetic field induced by changing electric flux
• Section 30.3 p. 839 shows that Ampere's law fails when we are near a charging capacitor.
• The current does not actually penetrate the area of curve C,
• but the line integral of B dot dl is not zero
• thus the line integral of B dot dl does not equal u_o I, since I = 0.
• Maxwell showed that the changing electric flux between the plates of the charging capacitor acted like a current, and he called it the 'displacement currrent' (p, 840).
• For cases like this, a changing electric flux (the displacement current) creates an induced magnetic field
• Part of the magnetic field may be created by a true current I
• Part of the magnetic field may be created by the 'displaeement current' (the changing electric flux)
• Or all of B may be created by I, or all of B may be created by changing electric flux, depending on the situation

• Light is a travelling combination of electric and magnetic fields which oscillate back and forth.(Chapter 34)
• We may think of the changing B flux creating an E field which is also changing
• Then the changing E flux creates an induced magnetic field which is also changing
• This leads to a succession of oscillations of combined E and B fields which we know as light
• It turns out that light
• has its E field perpendicular to the direction the light travels
• has its B field perpendicular to the direction the light travels
• has its E field perpendicular to the B field
• E and B are in phase: they get large together, zero together, and negative together
• If k^ is the direction of travel, then E^ x B^ = k^ ( E^ is a unit vector in the E direction)
• Some terms relevant to the energy generally
• Power = energy/ time
• Intensity = power/area
• Pressure = force/area
• For light, people use specialized terms
• The Poynting vector S gives the intensity: S = E x B / u_o (p. 939)
• Intensity is also called energy flux (meaning energy/time/area)
• For light, the SI optics term is irradiance instead of intensity (p. 940, and the rest of the book)
• In a 'plane wave'
• E oscillates only along one line; its magnitude is Eo
• B oscillates only along one line; its magnitude is Eo/c (c=speed of light)
• since Bo=Eo/c, the poynting vector magnitude is S = Eo^2/(u_o c)
• A beam of light carries
• energy U
• linear momentum p
• For a beam of light U = pc.
• Because c is 300 million m/s, p =U/c is a small quantity
• Force = m a = m dv/dt = d/dt (mv) = dp/dt
• Force = time rate of change of linear momentum
• When a light beam is absorbed,
• the body receives energy and a small amount of linear momentum
• A light beam striking a body exerts a small amount of force.
• You should be able to show that   power absorbed = (force exerted) c
• When a light beam is reflected the force exerted is 2 (beam power)/c
• Then the pressure exerted when a beam is reflected is
• pressure = 2 (intensity)/c or
• pressure = 2 (irradiance)/c