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Physics · Textbook solutions

Electromagnetic Waves

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 19 questions

Worked Examples

2 q

Solved Examples

Worked · 2
  1. Eg 8.1
    A plane electromagnetic wave of frequency 25 MHz25\,\text{MHz} travels in free space along the xx-direction. At a particular point in space and time, E=6.3 j^ V/m\mathbf{E} = 6.3\,\hat{\mathbf{j}}\,\text{V/m}. What is B\mathbf{B} at this point?
  2. Eg 8.2
    The magnetic field in a plane electromagnetic wave is given by By=(2×10−7) Tsin⁡(0.5×103x+1.5×1011t)B_y = (2 \times 10^{-7})\,\text{T} \sin\left(0.5 \times 10^{3} x + 1.5 \times 10^{11} t\right). (a) What is the wavelength and frequency of the wave? (b) Write an expression for the electric field.

Exercises

17 q
  1. Ex 8.1(a)
    Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm12\,\text{cm}, and separated by 5.0 cm5.0\,\text{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 A0.15\,\text{A}. (a) Calculate the capacitance and the rate of change of potential difference between the plates.
  2. Ex 8.1(b)
    Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm12\,\text{cm}, and separated by 5.0 cm5.0\,\text{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 A0.15\,\text{A}. (b) Obtain the displacement current across the plates.
  3. Ex 8.1(c)
    Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm12\,\text{cm}, and separated by 5.0 cm5.0\,\text{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 A0.15\,\text{A}. (c) Is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor? Explain.
  4. Ex 8.2(a)
    A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius R=6.0 cmR = 6.0\,\text{cm} has a capacitance C=100 pFC = 100\,\text{pF}. The capacitor is connected to a 230 V230\,\text{V} ac supply with a (angular) frequency of 300 rad s−1300\,\text{rad s}^{-1}. (a) What is the rms value of the conduction current?
  5. Ex 8.2(b)
    A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius R=6.0 cmR = 6.0\,\text{cm} has a capacitance C=100 pFC = 100\,\text{pF}. The capacitor is connected to a 230 V230\,\text{V} ac supply with a (angular) frequency of 300 rad s−1300\,\text{rad s}^{-1}. (b) Is the conduction current equal to the displacement current?
  6. Ex 8.2(c)
    A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius R=6.0 cmR = 6.0\,\text{cm} has a capacitance C=100 pFC = 100\,\text{pF}. The capacitor is connected to a 230 V230\,\text{V} ac supply with a (angular) frequency of 300 rad s−1300\,\text{rad s}^{-1}. (c) Determine the amplitude of B\mathbf{B} at a point 3.0 cm3.0\,\text{cm} from the axis between the plates.
  7. Ex 8.3
    What physical quantity is the same for X-rays of wavelength 10−10 m10^{-10}\,\text{m}, red light of wavelength 6800 A˚6800\,\text{\AA} and radiowaves of wavelength 500 m500\,\text{m}?
  8. Ex 8.4
    A plane electromagnetic wave travels in vacuum along zz-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz30\,\text{MHz}, what is its wavelength?
  9. Ex 8.5
    A radio can tune in to any station in the 7.5 MHz7.5\,\text{MHz} to 12 MHz12\,\text{MHz} band. What is the corresponding wavelength band?
  10. Ex 8.6
    A charged particle oscillates about its mean equilibrium position with a frequency of 109 Hz10^{9}\,\text{Hz}. What is the frequency of the electromagnetic waves produced by the oscillator?
  11. Ex 8.7
    The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0=510 nTB_0 = 510\,\text{nT}. What is the amplitude of the electric field part of the wave?
  12. Ex 8.8(a)
    Suppose that the electric field amplitude of an electromagnetic wave is E0=120 N/CE_0 = 120\,\text{N/C} and that its frequency is ν=50.0 MHz\nu = 50.0\,\text{MHz}. (a) Determine B0B_0, ω\omega, kk, and λ\lambda.
  13. Ex 8.8(b)
    Suppose that the electric field amplitude of an electromagnetic wave is E0=120 N/CE_0 = 120\,\text{N/C} and that its frequency is ν=50.0 MHz\nu = 50.0\,\text{MHz}. (b) Find expressions for E\mathbf{E} and B\mathbf{B}.
  14. Ex 8.9
    The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E=hνE = h\nu (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?
  15. Ex 8.10(a)
    In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0×1010 Hz2.0 \times 10^{10}\,\text{Hz} and amplitude 48 V m−148\,\text{V m}^{-1}. [Take c=3×108 m s−1c = 3 \times 10^{8}\,\text{m s}^{-1}.] (a) What is the wavelength of the wave?
  16. Ex 8.10(b)
    In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0×1010 Hz2.0 \times 10^{10}\,\text{Hz} and amplitude 48 V m−148\,\text{V m}^{-1}. [Take c=3×108 m s−1c = 3 \times 10^{8}\,\text{m s}^{-1}.] (b) What is the amplitude of the oscillating magnetic field?
  17. Ex 8.10(c)
    In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0×1010 Hz2.0 \times 10^{10}\,\text{Hz} and amplitude 48 V m−148\,\text{V m}^{-1}. [Take c=3×108 m s−1c = 3 \times 10^{8}\,\text{m s}^{-1}.] (c) Show that the average energy density of the E\mathbf{E} field equals the average energy density of the B\mathbf{B} field.