# signal plane

```1. A plane electromagnetic wave traveling in the positive direction of an x axis in
vacuum has components Ex = Ey = 0 and Ez = (2.0 V/m)cos[(&times;1015 s-1)(t－x/c)].
(a) What is the amplitude of the magnetic field component? (b) Parallel to which
axis does the magnetic field oscillate? (c) When the electric field component is in
the positive direction of the z axis at a certain point P, what is the direction of the
magnetic field component there?
Ans. (a) 6.7&times;10-9 T (b) y axis (c) –y direction
2. An airplane flying at a distance of 10 km from a radio transmitter receives a signal
of intensity 10 W/m2. What is the amplitude of the (a) electric and (b) magnetic
component of the signal at the airplane? (c) If the transmitter radiates uniformly
over a hemisphere, what is the transmission power?
Ans. (a) 8.7&times;10-2 V/m (b) 2.9&times;10-10 T (c) 6.3&times;103 W
3. The maximum electric field 10 m from an isotropic point source of light is 2.0
V/m. What are (a) the maximum value of the magnetic field and (b) the average
intensity of the light there? (c) What is the power of the source?
Ans. (a) 6.7&times;10-9 T (b) 5.3&times;10-3 W/m2 (c) 6.7 W
4. Radiation from the Sun reaching Earth (just outside the atmosphere) has an
intensity of 1.4 kW/m2. (a) Assuming that Earth (and its atmosphere) behaves like
a flat disk perpendicular to the Sun’s rays and that all the incident energy is
absorbed, calculate the force on Earth due to radiation pressure. (b) For
comparison, calculate the force due to the Sun’s gravitational attraction.
Ans. (a) 6.0&times;108 N (b) 3.6&times;1022 N
5. Prove, for a plane electromagnetic wave that is normally incident on a flat surface,
that the radiation pressure on the surface is equal to the energy density in the
incident beam. (This relation between pressure and energy density holds no matter
what fraction of the incident energy is reflected.)
6. In the figure, a laser beam of power 4.60 W and diameter D
= 3.00 mm is directed upward at one circular face (of
diameter d &lt; 2.60 mm) of a perfectly reflecting cylinder.
The cylinder is levitated because the upward radiation force
matches the downward gravitational force. If the cylinder’s
density is 1.20 g/cm3, what is its height H?
Ans. 3.69&times;10-7 m
7. A plane electromagnetic wave, with wavelength 3.0 m, travels in vacuum in the
positive direction of an x axis. The electric field, of amplitude 300 V/m, oscillates
parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c)
angular wave number of the wave? (d) What is the amplitude of the magnetic field
component? (e) Parallel to which axis does the magnetic field oscillate? (f) What
is the time-averaged rate of energy flow in watts per square meter associated with
this wave? The wave uniformly illuminates a surface of area 2.0 m2. If the surface
totally absorbs the wave, what are (g) the rate at which momentum is transferred
to the surface and (h) the radiation pressure on the surface?
Ans. (a) 1.0&times;108 Hz (b) 6.3&times;108 rad/s (c) 2.1 rad/m (d) 1.0&times;10-6 T
(e) positive z direction (f) 1.2&times;102 W/m2 (g) 8.0&times;10-7 N (h) 4.0&times;10-7 Pa
```