32. Electromagnetic Waves

(II) An electromagnetic wave has an electric field given by $\vec{E}=\hat{i}\left(2775\text{ V/m}\right)\sin \left[\right(0.053{\text{ m}}^{-1})z-(1.6\times {10}^7\text{ rad/s}\left)t\right]$.

a. What are the wavelength and frequency of the wave?

b. Write down an expression for the magnetic field.

If the electric field in an EM wave has a peak magnitude of 0.45 x 10^-4 V/m, what is the peak magnitude of the magnetic field strength?

(II) Estimate the average power output of the Sun, given that about 1350 W/m² reaches the upper atmosphere of the Earth.

Estimate the rms electric field in the sunlight that hits Mars, knowing that the Earth receives about 1350 W/m² and that Mars is 1.52 times farther from the Sun (on average) than is the Earth.

INT Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 500 nm?

What length of antenna would be appropriate for a portable device that could receive satellite TV?

(II) What size should the solar panel on a satellite orbiting Jupiter be if it is to collect the same amount of radiation from the Sun as a 1.0-m² solar panel on a satellite orbiting Earth? [Hint: Assume the inverse square law.]

What are E₀ and B₀ at a point 2.50 m from a light source whose output is 5.0 W? Assume the bulb emits radiation of a single frequency uniformly in all directions.

The diameter of the nucleus is about 10 fm. What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of 10 fm?

A radio station is allowed to broadcast at an average power not to exceed 25 kW. If an electric field amplitude of 0.020 V/m is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to detect this station.

A 2.0 cm×2.0 cm square loop of wire with resistance 0.010 Ω has one edge parallel to a long straight wire. The near edge of the loop is 1.0 cm from the wire. The current in the wire is increasing at the rate of 100 A/s. What is the current in the loop?

The diameter of the nucleus is about 10 fm. A simple model of the nucleus is that protons and neutrons are confined within a one-dimensional box of length 10 fm. What are the first three energy levels, in MeV, for a proton in such a box?

A parallel-plate, air-filled capacitor is being charged as in Fig. 29.23. The circular plates have radius 4.00 cm, and at a particular instant the conduction current in the wires is 0.520 A. (c) What is the induced magnetic field between the plates at a distance of 2.00 cm from the axis? (d) At 1.00 cm from the axis?

If a galaxy is traveling away from us at 2.2% of the speed of light, roughly how far away is it?