Lunds Universitet
Andreas Wacker, Yousef Yousefi
2015-11-16
Exercises to Electrodynamics, Week 3
Homework to be handed in on Nov. 24 in Yousefs mailbox
Exercise 1: Radial dependence of electric fields
Discuss why the fields drop as 1/r2 in electro/magneto-statics and why 1/r holds for radiation
fields.
Exercise 2: Energy balance in LC-circuit
a) Show that the energy stored in a capacitor with capacity C is UC = 12 CU 2
b) Show that the energy stored in an inductor with the induction coefficient L is UL = 12 LI 2
c) Discuss the energy balance in an LC-circuit. How is the energy transferred between the
capacitor and the inductor?
Exercise 3 (Homework): Linear antenna as dipole
By Taylor expanding, show that the far fields for the linear antenna, using the current density
from section 3.4 of the lecture sketch, equal dipole fields for L λ.
Exercise 4 (Homework): Classical model of an atom
Assume the electron to be a classical particle rotating in circles around the nucleus in the
x, y plane with frequency ω and radius r (This is often called the Rutherford model). This
constitutes an electrical dipole moment p(t) = re(ex + iey )e−iωt .
a) Calculate the energy loss of the electron as a function of r and ω. The radiated power can
be obtained from Equation (9.24) in Jackson.
2 2
2
e2
. Evaluate dr/dt
b) From classical mechanics we have me ω 2 r = 4πe0 r2 and E = me ω2 r − 4π
0r
on the basis of the energy loss of part a).
c) How long does it take until the electron falls into the nucleus if it starts at r0 = 0.1 nm?