32. Electromagnetic Waves

What is the intensity of an electromagnetic wave with a peak electric field strength of $125V/m$? (Assume the wave is in vacuum and use $c=3.00\times {10}^{8}m/s$ and $\epsilon 0_{}=8.85\times {10}^{-}C{2}^{/}$)

A point source light bulb emits uniformly in all directions with a total power output of $60W$. At a distance of $2.0m$ from the bulb, what is the light intensity?

If a microwave oven operates at a frequency of $2.4\times 109^{\mathrm{Hz}}$ and the intensity inside the oven is $2800 W/m^2$, what is the amplitude of the electric field of the microwaves inside the oven? (Assume the speed of light $c=3.0\times 108^m/s$ and vacuum permittivity $\epsilon =8.85\times 10{-12}^F/m$.)

A 100 W lightbulb actually emits around only 10 W of light. What is the intensity of the light 1 cm away if the light is emitted perfectly spherically? What is the magnitude of the electric field emitted by the lightbulb? What about the magnetic field?

What is the total energy density in an electromagnetic wave of intensity 1000 W/m²?

When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5×10⁹ km from the earth. Its radio transmitter, with which it sent back data and s, broadcast with a mere 21 W of power. Assuming that the transmitter broadcast equally in all directions, What signal intensity was received on the earth?

Consider current I passing through a resistor of radius r, length L, and resistance R. Determine the strength and direction of the Poynting vector at the surface of the resistor.

Consider current I passing through a resistor of radius r, length L, and resistance R. Show that the flux of the Poynting vector (i.e., the integral of $\overrightarrow{S}\cdot d\overrightarrow{A}$) over the surface of the resistor is I²R. Then give an interpretation of this result.

A radio receiver can detect signals with electric field amplitudes as small as 300 μV/m. What is the intensity of the smallest detectable signal?

A microwave beam with a wavelength of 1.5 cm has an intensity of 25 W/m². What is the magnetic field amplitude?

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are $\overrightarrow{E}=(200\hat{i}+300\hat{j}-50\hat{k})\text{ V/m}$ and $\overrightarrow{B}=B_0(7.3\hat{i}-7.3\hat{j}+a\hat{k})\mu \text{T}$. What are the values of $a$ and $B_0$?