Chapter 8 Solutions — Electromagnetic Waves

Exercises

1. 1.
   Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.

   • (a) Calculate the capacitance and the rate of change of potential difference between the plates.
   • (b) Obtain the displacement current across the plates.
   • (c) Is…
2. 2.
   A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s⁻¹.

   • (a) What is the rms value of the conduction current?
   • (b) Is the conduction current equal to the displacement current?
   • (c) Determine the amplitude of B at a point 3.0 cm from the axis…
3. 3.
   What physical quantity is the same for X-rays of wavelength 10⁻¹⁰ m, red light of wavelength 6800 Å and radiowaves of wavelength 500 m?
4. 4.
   A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?
5. 5.
   A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
6. 6.
   A charged particle oscillates about its mean equilibrium position with a frequency of 10⁹ Hz. What is the frequency of the electromagnetic waves produced by the oscillator?
7. 7.
   The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B₀ = 510 nT. What is the amplitude of the electric field part of the wave?
8. 8.
   Suppose that the electric field amplitude of an electromagnetic wave is E₀ = 120 N/C and that its frequency is ν = 50.0 MHz.

   • (a) Determine B₀, ω, k, and λ.
   • (b) Find expressions for E and B.
9. 9.
   The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = hν (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?
10. 10.
    In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10¹⁰ Hz and amplitude 48 V m⁻¹.

    • (a) What is the wavelength of the wave?
    • (b) What is the amplitude of the oscillating magnetic field?
    • (c) Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 × 10⁸ m s⁻¹.]