Suppose a 25-kW radio station emits EM waves uniformly in all directions. What is the rms voltage induced in a 1.0-m-long vertical car antenna (c) 1.0 km away, (d) 50 km away?

What is the maximum power level of a radio station so as to avoid electrical breakdown of air at a distance of 0.75 m from the transmitting antenna? Assume the antenna is a point source. Air breaks down in an electric field of about 3 x 10⁶ V/m.

Show that displacement current, ε₀ (dΦE/dt), has the SI units of amperes.

How large an emf (rms) will be generated in an antenna that consists of a circular coil 2.2 cm in diameter having 280 turns of wire, when an EM wave of frequency 810 kHz transporting energy at an average rate of 1.0 x 10⁻⁴ W/m² passes through it? [Hint: You can use Eq. 29–4 (for a generator) because that equation can be applied to an observer moving with the generator’s coil as it rotates at ω = 2𝝅f with f the frequency of the magnetic field.]

Imagine that a steady current I flows in a straight cylindrical wire of radius R₀ and resistivity ρ.

(a) If the current is then changed at a rate dI/dt, show that a displacement current ID exists in the wire of magnitude ε₀ρ(dI/dt).

(b) If the current in a copper wire is changed at the rate of 1.0 A/ms, determine the magnitude of ID.

(c) Determine the magnitude of the magnetic field BD created by ID at the surface of a copper wire with R₀ = 1.00 mm. Compare (as a ratio) BD with the field created at the surface of the wire by a steady current of 1.0 A.

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.