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

(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?

Why do some microwave ovens rotate the food container? Suppose the metal walls form a rectangular cavity of dimensions 37 cm x 37 cm x 20 cm. When 2.45-GHz microwaves are continuously introduced into this cavity, reflection of incident waves from the walls sets up standing waves with nodes at the walls. Along the 37-cm dimension of the oven, how many nodes exist (excluding the nodes at the wall) and what is the distance between adjacent nodes? (No heating occurs at these nodes, so rotating the food container gives more even heating of the food.)

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.

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.

Suppose that a right-moving EM wave overlaps with a left-moving EM wave so that, in a certain region of space, the total electric field in the y direction and magnetic field in the z direction are given by Eᵧ = E₀ sin(kx - ωt) + E₀ sin(kx + ωt) and Bz = B₀ sin(kx - ωt) - B₀ sin(kx + ωt). Determine the Poynting vector and find the x locations at which it is zero at all times.

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. (a) What is the rate of change of flux through a circle with radius r₁ inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? (b) Find the magnitude of the induced electric field inside the solenoid, at a distance r₁ from its axis. Show the direction of this field in a diagram. (c) What is the magnitude of the induced electric field outside the solenoid, at a distance r₂ from the axis?