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A laser beam

The beam from a small laboratory laser typically has an intensity of about 1.0 × 10 −3 W/m 2 . Assuming that the beam is composed of plane waves, calculate the amplitudes of the electric and magnetic fields in the beam.

Strategy

Use the equation expressing intensity in terms of electric field to calculate the electric field from the intensity.

Solution

From [link] , the intensity of the laser beam is

I = 1 2 c ε 0 E 0 2 .

The amplitude of the electric field is therefore

E 0 = 2 c ε 0 I = 2 ( 3.00 × 10 8 m/s ) ( 8.85 × 10 −12 F/m ) ( 1.0 × 10 −3 W/m 2 ) = 0.87 V/m .

The amplitude of the magnetic field can be obtained from [link] :

B 0 = E 0 c = 2.9 × 10 −9 T .
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Light bulb fields

A light bulb emits 5.00 W of power as visible light. What are the average electric and magnetic fields from the light at a distance of 3.0 m?

Strategy

Assume the bulb’s power output P is distributed uniformly over a sphere of radius 3.0 m to calculate the intensity, and from it, the electric field.

Figure shows a light bulb in the centre illuminating a circular area around it. This area has a radius of 3 m.

Solution

The power radiated as visible light is then

I = P 4 π r 2 = c ε 0 E 0 2 2 , E 0 = 2 P 4 π r 2 c ε 0 = 2 5.00 W 4 π ( 3.0 m ) 2 ( 3.00 × 10 8 m/s ) ( 8.85 × 10 −12 C 2 /N · m 2 ) = 5.77 N/C, B 0 = E 0 / c = 1.92 × 10 −8 T .

Significance

The intensity I falls off as the distance squared if the radiation is dispersed uniformly in all directions.

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Radio range

A 60-kW radio transmitter on Earth sends its signal to a satellite 100 km away ( [link] ). At what distance in the same direction would the signal have the same maximum field strength if the transmitter’s output power were increased to 90 kW?

A point is labeled radio source. A small square labeled A1 is in the path of the lines radiating from the radio source. The lines continue from the corners of A1 and reach A2, a slightly bigger square. A1 is at a distance r1 from the source and A2 is at a distance R2.
In three dimensions, a signal spreads over a solid angle as it travels outward from its source.

Strategy

The area over which the power in a particular direction is dispersed increases as distance squared, as illustrated in the figure. Change the power output P by a factor of (90 kW/60 kW) and change the area by the same factor to keep I = P A = c ε 0 E 0 2 2 the same. Then use the proportion of area A in the diagram to distance squared to find the distance that produces the calculated change in area.

Solution

Using the proportionality of the areas to the squares of the distances, and solving, we obtain from the diagram

r 2 2 r 1 2 = A 2 A 1 = 90 W 60 W , r 2 = 90 60 ( 100 km ) = 122 km .

Significance

The range of a radio signal is the maximum distance between the transmitter and receiver that allows for normal operation. In the absence of complications such as reflections from obstacles, the intensity follows an inverse square law, and doubling the range would require multiplying the power by four.

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Summary

  • The energy carried by any wave is proportional to its amplitude squared. For electromagnetic waves, this means intensity can be expressed as
I = c ε 0 E 0 2 2

where I is the average intensity in W/m 2 and E 0 is the maximum electric field strength of a continuous sinusoidal wave. This can also be expressed in terms of the maximum magnetic field strength B 0 as

I = c B 0 2 2 μ 0

and in terms of both electric and magnetic fields as

I = E 0 B 0 2 μ 0 .

The three expressions for I avg are all equivalent.

Conceptual questions

When you stand outdoors in the sunlight, why can you feel the energy that the sunlight carries, but not the momentum it carries?

The amount of energy (about 100 W/m 2 ) is can quickly produce a considerable change in temperature, but the light pressure (about 3.00 × 10 −7 N/m 2 ) is much too small to notice.

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Questions & Answers

what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Abdul
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
Gamma
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
TONEJIT Reply
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
DRASHTI Reply
what is an ideal gas?
Justine Reply
What is meant by zero Kelvin ?
Justine
Why does water cool when put in the pot ?
Justine
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
rupendra
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
Srabon
types of thermometer?
yemisi Reply
thermometer, Radiation thermometer and vapour pressure thermometer.liquid thermometer use thermometric liquid like mercury ,alcohol etc.
rupendra
liqid thermometer ,gas thermometer, resitance thermometer,thermo electric thermometer , radiation thermometer andvapour pressure thermometer
rupendra
calculate the quantity of heat required to rise the temperature of 1gmail of ice _10 to 110
Dargu Reply
A 40cm tall glass is filled with water to a depth of 30cm. A.what is the gauge pressure at the bottom of the glass? B.what is the absolute pressure at the bottom of the glass?
Abdulaziz Reply
A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
A wave is a periodic disturbance which travel with a finite velocity and remains unchanged in type as it travels.
Justine
What's a wave motion?
Justine
What is charge bodies
Oje Reply
which have free elections
Usman
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Pak
Charge bodies are those which have free electons
Pak
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
eugene
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
Shahid
it's a line used to represent a complex electrical quantity as a vector
Gift Reply
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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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