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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

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Chovwe Reply
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Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
what is vector quantity
Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
Jack Reply
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Chinaza Reply
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
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Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
Ajayi Reply
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
Gabriel Reply
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
Gabriel Reply
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Mavis
I can't even understand the question
Ademiye
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Gabriel
mu/y³ u>v²k² uk²/√u-vk please help me out
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
Imtiaz Reply
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Ademiye
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
Isaac Reply
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
Mildred Reply
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
Ademiye
method of polarization
Ajayi
What is atomic number?
Makperr Reply
The number of protons in the nucleus of an atom
Deborah
type of thermodynamics
Yinka Reply
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
Taheer Reply
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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