The beam from a small laboratory laser typically has an intensity of about
$1.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-3}}{\phantom{\rule{0.2em}{0ex}}\text{W/m}}^{2}$ . 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.
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?
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
$I=\frac{P}{A}=\frac{c{\epsilon}_{0}{E}_{0}^{2}}{2}$ 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
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.
The energy carried by any wave is proportional to its amplitude squared. For electromagnetic waves, this means intensity can be expressed as
$I=\frac{c{\epsilon}_{0}{E}_{0}^{2}}{2}$
where
I is the average intensity in
${\text{W/m}}^{2}$ 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
$I=\frac{c{B}_{0}^{2}}{2{\mu}_{0}}$
and in terms of both electric and magnetic fields as
$I=\frac{{E}_{0}{B}_{0}}{2{\mu}_{0}}.$
The three expressions for
${I}_{\text{avg}}$ 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
${100\phantom{\rule{0.2em}{0ex}}\text{W/m}}^{2}$ ) is can quickly produce a considerable change in temperature, but the light pressure (about
$3.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-7}}{\text{N/m}}^{2}$ ) is much too small to notice.
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)
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.
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?
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
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
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