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.
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K
kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'