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Electromagnetic Waves EXERCISES Solutions
- Q8.1(a): 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 0.15A. (a) Calculate the capacitance and the rate of change of potential difference between the plates.
- Q8.1(a): 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 0.15A. (a) Calculate the capacitance and the rate of change of potential difference between the plates.
- Q8.1(b): 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 0.15A. (b) Obtain the displacement current across the plates.
- Q8.1(b): 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 0.15A. (b) Obtain the displacement current across the plates.
- Q8.1(c): 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 0.15A. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.
- Q8.1(c): 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 0.15A. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.
- Q8.10(a): In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $2.0 \times 10^{10}$ Hz and amplitude $48 \text{ V m}^{-1}$. (a) What is the wavelength of the wave?
- Q8.10(a): In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $(2.0 \times 10^{10} \text{ Hz})$ and amplitude $(48 \text{ V m}^{-1})$. (a) What is the wavelength of the wave?
- Q8.10(b): In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $2.0 \times 10^{10}$ Hz and amplitude $48 \text{ V m}^{-1}$. (b) What is the amplitude of the oscillating magnetic field?
- Q8.10(b): In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $(2.0 \times 10^{10} \text{ Hz})$ and amplitude $(48 \text{ V m}^{-1})$. (b) What is the amplitude of the oscillating magnetic field?
- Q8.10(c): In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $2.0 \times 10^{10}$ Hz and amplitude $48 \text{ V m}^{-1}$. (c) Show that the average energy density of the $E$ field equals the average energy density of the $B$ field. [$c = 3 \times 10^8 \text{ m s}^{-1}$.]
- Q8.10(c): In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of $(2.0 \times 10^{10} \text{ Hz})$ and amplitude $(48 \text{ V m}^{-1})$. (c) Show that the average energy density of the $(E)$ field equals the average energy density of the $(B)$ field. [$(c = 3 \times 10^{8} \text{ m s}^{-1})$.]
- Q8.2(a): 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 $300 \text{ rad s}^{-1}$. (a) What is the rms value of the conduction current?
- Q8.2(a): A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius $(R = 6.0 \text{ cm})$ has a capacitance $(C = 100 \text{ pF})$. The capacitor is connected to a 230 V ac supply with a (angular) frequency of $(300 \text{ rad s}^{-1})$. (a) What is the rms value of the conduction current?
- Q8.2(b): 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 $300 \text{ rad s}^{-1}$. (b) Is the conduction current equal to the displacement current?
- Q8.2(b): A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius $(R = 6.0 \text{ cm})$ has a capacitance $(C = 100 \text{ pF})$. The capacitor is connected to a 230 V ac supply with a (angular) frequency of $(300 \text{ rad s}^{-1})$. (b) Is the conduction current equal to the displacement current?
- Q8.2(c): 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 $300 \text{ rad s}^{-1}$. (c) Determine the amplitude of $B$ at a point 3.0 cm from the axis between the plates.
- Q8.2(c): A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius $(R = 6.0 \text{ cm})$ has a capacitance $(C = 100 \text{ pF})$. The capacitor is connected to a 230 V ac supply with a (angular) frequency of $(300 \text{ rad s}^{-1})$. (c) Determine the amplitude of $(B)$ at a point 3.0 cm from the axis between the plates.
- Q8.3: 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?
- Q8.3: What physical quantity is the same for X-rays of wavelength $(10^{-10} \text{ m})$, red light of wavelength $(6800 \text{ Å})$ and radiowaves of wavelength 500m?
- Q8.4: 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?
- Q8.4: 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?
- Q8.5: A radio can tune in to any station in the $7.5$ MHz to $12$ MHz band. What is the corresponding wavelength band?
- Q8.5: A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
- Q8.6: A charged particle oscillates about its mean equilibrium position with a frequency of $10^9$ Hz. What is the frequency of the electromagnetic waves produced by the oscillator?
- Q8.6: A charged particle oscillates about its mean equilibrium position with a frequency of $(10^{9} \text{ Hz})$. What is the frequency of the electromagnetic waves produced by the oscillator?
- Q8.7: The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $B_0 = 510$ nT. What is the amplitude of the electric field part of the wave?
- Q8.7: The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is $(B_{0} = 510 \text{ nT})$. What is the amplitude of the electric field part of the wave?
- Q8.8(a): Suppose that the electric field amplitude of an electromagnetic wave is $E_0 = 120$ N/C and that its frequency is $\nu = 50.0$ MHz. (a) Determine, $B_0, \omega, k$, and $\lambda$.
- Q8.8(a): Suppose that the electric field amplitude of an electromagnetic wave is $(E_{0} = 120 \text{ N/C})$ and that its frequency is $(n = 50.0 \text{ MHz})$. (a) Determine, $(B_{0})$, $(\omega)$, $(k)$, and $(\lambda)$.
- Q8.8(b): Suppose that the electric field amplitude of an electromagnetic wave is $E_0 = 120$ N/C and that its frequency is $\nu = 50.0$ MHz. (b) Find expressions for $E$ and $B$.
- Q8.8(b): Suppose that the electric field amplitude of an electromagnetic wave is $(E_{0} = 120 \text{ N/C})$ and that its frequency is $(n = 50.0 \text{ MHz})$. (b) Find expressions for $(E)$ and $(B)$.
- Q8.9: The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula $E = h\nu$ (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?
- Q8.9: The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula $(E = h\nu)$ (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?
Chapters in CBSE - Class 12 Physics
- Electric Charges and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics
- Communication Systems
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