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

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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

what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
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