Download Series 9 - Problems

Physics III
Prof. Dr. Simon Lilly
WS 2005/06
Series 9 - Problems
Tips: 12. January 2006 / Hand in: 19. January 2006 / Return: 26. January 2006
1
Displacement current
In a certain volume, the electric field changes according to
~ =E
~ 0 sin(ωt)
E
−1
with |E0 | = 2×10−2 N
. What is the maximum displacement current through
C and ω = 500 rad s
2
an area of A = 2 m that is perpendicular to the electric field?.
2
Spacecraft propulsion with radiation pressure
Some science-fiction authors propose that one could do space travel by a radiation pressure propulsion. Imagine a space craft with a gigantic sail in order to capture the radiation from a star as
shown in the picture.
a) What is the acceleration a of a space craft with mass m that has a sail with the area A. The
spacecraft is at a distance r from a star which radiates with power in electromagnetic waves
PS . All the electromagnetic radiation is absorbed by the sail. Hint: remember from special
relativity the relation between Energy E and momentum p of a mass less particle (as the
photon).
b) What changes if some of the radiation is reflected by the sail back towards the star?
c) Given we start at a distance r0 from the star with a radial velocity of v0 . What is the
velocity v1 of the spacecraft at a distance r1 ? Neglect the gravitational force from the star.
This idea is now no longer only science fiction! There is a solar sailing project called Cosmos 1
and more information can be found on the web: www.planetary.org/solarsail/
1
3
Electromagnetic wave
The electric field of an electromagnetic wave is given by


0
~ =  E0 sin(kx − ωt)  .
E
E0 cos(kx − ωt)
~ that belongs to this electromagnetic wave.
a) Calculate the magnetic field B
b) What is the relation between the amplitude of the magnetic field B0 and the amplitude of
the electric field E0 ?
~ · B?
~
c) What is the scalar product E
~ × B?
~
d) What is the vector product E
e) What is the behaviour of this wave?
4
Cosmic microwave background radiation
Of all the electromagnetic energy in the universe, by far the largest amount is in the form of waves
with wavelength in the millimeter range. This is the cosmic microwave background radiation
discovered by Penzias and Wilson in 1965. In the picture you can see an all sky view of the
cosmic microwave background. It apparently fills all the space including the vast space between
galaxies, with an energy density of w = 4.172 × 10−14 J m−3 . This energy density corresponds to
a temperature of T = 2.725 K. Across the sky, only very small fluctuations in the temperature
can be observed, i.e. the universe has nearly everywhere the same background temperature!
What is the maximum strength of the electric field E0 respectively of the magnetic field B0 of this
cosmic microwave background radiation?
2