Problem 1:

(a)  Compare the intensity of a light bulb at a distance of 6 m from it to the intensity at 2 m from it.  Repeat this comparison for laser light.  Explain fully but briefly.
(b)  Compute the electric field corresponding to a focused light intensity of I = 10¹²W/cm², and compare the result with the electric field experienced by the electron in a Hydrogen atom.

Problem 2:

Electrons in a computer monitor CRT are accelerated to a final kinetic energy of 30 keV over a distance of 1 cm, then are rapidly decelerated to zero speed in collisions with the screen phosphor.  Assume both acceleration and deceleration are constant.  Consider the energy radiated by accelerated electrons (which has nothing directly to do with the light emitted by the phosphor).
(a)  Can this problem be treated non-relativistically?  Explain why or why not.
(b)  Develop an expression for the ratio r of the energy radiated during the acceleration phase, E_rad, to the final kinetic energy E_kin, assuming constant acceleration a.  Also calculate a numeric value for r under the conditions pertaining to the acceleration of electrons in the monitor CRT described above.
(c)  Again assuming constant acceleration, estimate the maximum total fraction of kinetic energy that is radiated during the stopping of the electrons in the phosphor, and from that, the average power radiated per stopped electron in watts.  Assume all the kinetic energy is consumed in single collisions in a distance of 0.05 nm within single atoms of the phosphor.

Problem 3:

(a) An electron orbits initially, at time t = 0 around a proton at a radius a₀ equal to the Bohr radius.  Using classical mechanics and classical electromagnetism derive an expression for the time it takes for the radius of the orbiting electron to decrease to zero due to radiation.  Here you may assume that the energy loss per revolution is small compared to the total energy of the atom.
(b)  What implication can you draw from this calculation?  Give a qualitative argument on the need to modify the above estimate.          

Problem 4:

Consider a linear antenna of length d (d << l) with a narrow gap in the center for the purposes of excitation.  Assume that the current is sinusoidal and in the same direction in each half of the antenna, having a value of I₀ at the gap and falling linearly to zero at the ends.  Find the power radiated in the electric dipole approximation.

Problem 5:

Starting with Maxwell’s Equations:
(a)  Derive the wave equations for a light wave in vacuum.  Write out solutions for these equations for E and B.
(b)  Show that the electric and magnetic fields are in phase, perpendicular to each other and perpendicular to the direction of motion.
(c)  Determine the relative magnitude of the E and B fields.