# 24.4 Energy in electromagnetic waves  (Page 3/6)

 Page 3 / 6

An AM radio transmitter broadcasts 50.0 kW of power uniformly in all directions. (a) Assuming all of the radio waves that strike the ground are completely absorbed, and that there is no absorption by the atmosphere or other objects, what is the intensity 30.0 km away? (Hint: Half the power will be spread over the area of a hemisphere.) (b) What is the maximum electric field strength at this distance?

Suppose the maximum safe intensity of microwaves for human exposure is taken to be $1\text{.}\text{00 W}{\text{/m}}^{2}$ . (a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection. (b) What is the maximum electric field strength at the safe intensity? (Note that early radar units leaked more than modern ones do. This caused identifiable health problems, such as cataracts, for people who worked near them.)

(a) 89.2 cm

(b) 27.4 V/m

A 2.50-m-diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of $7\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\mu V/m$ . (See [link] .) (a) What is the intensity of this wave? (b) What is the power received by the antenna? (c) If the orbiting satellite broadcasts uniformly over an area of $1\text{.}\text{50}×{\text{10}}^{\text{13}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{2}$ (a large fraction of North America), how much power does it radiate?

Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of $1\text{.}\text{00}×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{V}/\text{m}$ for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c) What energy does it deliver on a $1\text{.}\text{00}{\text{-mm}}^{2}$ area?

(a) 333 T

(b) $1\text{.}\text{33}×{\text{10}}^{\text{19}}\phantom{\rule{0.25em}{0ex}}{\text{W/m}}^{2}$

(c) 13.3 kJ

Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity ( ${I}_{0}={2I}_{\text{ave}}$ ), using either the fact that ${E}_{0}=\sqrt{2}{E}_{\text{rms}}$ , or ${B}_{0}=\sqrt{2}{B}_{\text{rms}}$ , where rms means average (actually root mean square, a type of average).

Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects. (a) Show that the intensity is inversely proportional to ${r}^{2}$ , the distance from the source squared. (b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to $r$ .

(a) $I=\frac{P}{A}=\frac{P}{4\pi {r}^{2}}\propto \frac{1}{{r}^{2}}$

(b) ${\mathrm{I\propto E}}_{0}^{2}\text{,}\phantom{\rule{0.25em}{0ex}}{B}_{0}^{2}⇒{E}_{0}^{2}\text{,}\phantom{\rule{0.25em}{0ex}}{B}_{0}^{2}\propto \frac{1}{{r}^{2}}⇒{E}_{0},\phantom{\rule{0.25em}{0ex}}{B}_{0}\propto \frac{1}{r}$

Integrated Concepts

An $\text{LC}$ circuit with a 5.00-pF capacitor oscillates in such a manner as to radiate at a wavelength of 3.30 m. (a) What is the resonant frequency? (b) What inductance is in series with the capacitor?

Integrated Concepts

What capacitance is needed in series with an $\text{800}-\mu \text{H}$ inductor to form a circuit that radiates a wavelength of 196 m?

13.5 pF

#### Questions & Answers

What does mean ohms law imply
what is matter
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
Alo
the time rate of increase in velocity is called
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
how to solve pressure?
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
what is accuracy and precision
How does a current follow?
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
what is Atom? what is molecules? what is ions?
What is a molecule
Is a unit of a compound that has two or more atoms either of the same or different atoms
Justice
A molecule is the smallest indivisible unit of a compound, Just like the atom is the smallest indivisible unit of an element.
Rachel
what is a molecule?
Vineeta
what is a vector
A quantity that has both a magnitude AND a direction. E.g velocity, acceleration, force are all vector quantities. Hope this helps :)
deage
what is the difference between velocity and relative velocity?
Mackson
Velocity is the rate of change of displacement with time. Relative velocity on the other hand is the velocity observed by an observer with respect to a reference point.
Chuks
what do u understand by Ultraviolet catastrophe?
Rufai
A certain freely falling object, released from rest, requires 1.5seconds to travel the last 30metres before it hits the ground. (a) Find the velocity of the object when it is 30metres above the ground.
Mackson
A vector is a quantity that has both magnitude and direction
Rufus
the velocity Is 20m/s-2
Rufus
derivation of electric potential
V = Er = (kq/r^2)×r V = kq/r Where V: electric potential.
Chuks
what is the difference between simple motion and simple harmonic motion ?
syed
hi
Peace
hi
Rufus
hi
Chip
simple harmonic motion is a motion of tro and fro of simple pendulum and the likes while simple motion is a linear motion on a straight line.
Muinat
a body acceleration uniform from rest a 6m/s -2 for 8sec and decelerate uniformly to rest in the next 5sec,the magnitude of the deceleration is ?
The wording not very clear kindly
Moses
6
Leo
9.6m/s2
Jolly
the magnitude of deceleration =-9.8ms-2. first find the final velocity using the known acceleration and time. next use the calculated velocity to find the size of deceleration.
Mackson
wrong
Peace
-3.4m/s-2
Justice
Hi
Abj
Firstly, calculate final velocity of the body and then the deceleration. The final ans is,-9.6ms-2
Muinat
8x6= 48m/-2 use v=u + at 48÷5=9.6
Lawrence
can i define motion like this motion can be define as the continuous change of an object or position
Any object in motion will come to rest after a time duration. Different objects may cover equal distance in different time duration. Therefore, motion is defined as a change in position depending on time.
Chuks