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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?

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Suppose the maximum safe intensity of microwaves for human exposure is taken to be 1 . 00 W /m 2 size 12{1 "." "00""W/m" rSup { size 8{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

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A 2.50-m-diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of 7 . 50 μ V/m size 12{7 "." "50" mV/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 . 50 × 10 13 m 2 size 12{1 "." "50"´"10" rSup { size 8{"13"} } " m" rSup { size 8{2} } } {} (a large fraction of North America), how much power does it radiate?

A large, round dish antenna looking like a giant white saucer is shown. It rests on a pillar like structure based on the ground. It is shown to receive TV signals in the form of electromagnetic waves shown as wavy arrows.
Satellite dishes receive TV signals sent from orbit. Although the signals are quite weak, the receiver can detect them by being tuned to resonate at their frequency.
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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 . 00 × 10 11 V / m size 12{1 "." "00"´"10" rSup { size 8{"11"} } " V"/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 . 00 -mm 2 size 12{1 "." "00""-mm" rSup { size 8{2} } } {} area?

(a) 333 T

(b) 1 . 33 × 10 19 W/m 2 size 12{1 "." "33"´"10" rSup { size 8{"19"} } "W/m" rSup { size 8{2} } } {}

(c) 13.3 kJ

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Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity ( I 0 = 2 I ave size 12{I rSub { size 8{0} } =2I rSub { size 8{"ave"} } } {} ), using either the fact that E 0 = 2 E rms size 12{E rSub { size 8{0} } = sqrt {2} E rSub { size 8{"rms"} } } {} , or B 0 = 2 B rms size 12{B rSub { size 8{0} } = sqrt {2} B rSub { size 8{"rms"} } } {} , where rms means average (actually root mean square, a type of average).

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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 size 12{r rSup { size 8{2} } } {} , the distance from the source squared. (b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to r size 12{r} {} .

(a) I = P A = P r 2 1 r 2 size 12{I= { {P} over {A} } = { {P} over {4π r rSup { size 8{2} } } } prop { {1} over {r rSup { size 8{2} } } } } {}

(b) I∝E 0 2 , B 0 2 E 0 2 , B 0 2 1 r 2 E 0 , B 0 1 r

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Integrated Concepts

An LC size 12{ ital "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?

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Integrated Concepts

What capacitance is needed in series with an 800 μ H size 12{"800"-mH} {} inductor to form a circuit that radiates a wavelength of 196 m?

13.5 pF

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Questions & Answers

How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Larissa Reply
How do you convert 0.0045kgcm³ to the si unit?
EDYKING Reply
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
Falana Reply
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
what the meaning of continuum
Akhigbe Reply
What state of matter is fire
Thapelo Reply
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Thapelo Reply
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
what is the relativity of physics
Paul Reply
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
Anthony Reply
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
Mehadi
hello
King
Explain dopplers effect
Jennifer Reply
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Alabi Reply
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
Calculation of kinetic and potential energy
dion Reply
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
Nworu Reply
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
PROMISE Reply
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat
what does fluorine do?
Cheyanne Reply
strengthen and whiten teeth.
Gia
a simple pendulum make 50 oscillation in 1minute, what is it period of oscillation?
Nansing Reply
length of pendulm?
bhat
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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