Intensity of EM Waves Practice Problems

For an electromagnetic wave at a particular location, the electric field is represented as E = (100 i + 200 j - 50k) V/m, while the magnetic field is denoted as B = (5.2 i - 8.3 j - b k)T at the same instance. Determine the Poynting vector at this particular moment.

In a science laboratory, you have a thin, black plastic film with dimensions of 8.0 by 8.0 inches and a mass of 0.42 g. You use an advanced laser system capable of producing a precisely controlled, upward-facing beam. Determine the minimum intensity required to suspend the plastic film in mid-air horizontally.

Given an electromagnetic wave with an intensity of 2000 W/m², determine its total energy density.

A newly established base 6.0 × 10 ⁹ km from Earth has set up communication with Earth. The base's 50 W transmitter sends data to Earth. Assuming equal broadcast in all directions, estimate the intensity of the signal received on Earth from the newly established base.

Consider a cylindrical cable with a radius of 'a', carrying a constant current 'I' and having a resistance 'R.' This current generates a magnetic field of strength 'B' surrounding the cable and an electric field 'E' which is uniform everywhere. Determine the Poynting vector's strength and direction at the cable's surface.

A cylindrical wire of radius a, length b, and resistance R carries a current I. If the power per unit area carried by an electric and magnetic field at the surface of the wire is (I²R) / (2πab), what should be the flux of the Poynting vector over the surface of the wire?

A research facility is testing a highly sensitive electromagnetic wave detector capable of detecting signals with a minimum electric field amplitude of 500 μV/m. Determine the intensity of the weakest electromagnetic wave the detector can perceive.

A radar signal is being used for remote sensing. The signal has an intensity of 50 W/m² at the source. Determine the amplitude of the magnetic field associated with this radar signal.

Consider an electromagnetic wave traveling through space. At a given time and position, the wave is characterized by E = E ₀ (-25 î - 29 ĵ + E_z k̂) V/m and B = (-4.8 î + 5.0 ĵ + 4.6 k̂ ) μT. Calculate E₀and E_z