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Question 8.1 Figure 8.6 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 charge of potential
difference between the plates.
(b) Obtain the displacement current across the plates.
(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the
capacitor? Explain
Question 8.2 A parallel plate capacitor (Fig. 8.7) 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
between the plates.
Question 8.3 What physical quantity is the same for X-rays of wavelength
10–10 m, red light of wavelength 6800 Å and radiowaves of wavelength
500m?
Question 8.4 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?
Question 8.5 A radio can tune in to any station in the 7.5 MHz to 12 MHz band.
What is the corresponding wavelength band?
Question 8.6 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?
Question 8.7 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?
Question 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.
Question 8.9 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?
Question 8.10 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.]
Question 8.11 Suppose that the electric field part of an electromagnetic wave in
vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) y + (5.4 × 106 rad/s)t]}ˆi .
(a) What is the direction of propagation?
(b) What is the wavelength λ ?
(c) What is the frequency ν
?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave.
Question 8.12 About 5% of the power of a 100 W light bulb is converted to visible
radiation. What is the average intensity of visible radiation
(a) at a distance of 1m from the bulb?
(b) at a distance of 10 m?
Assume that the radiation is emitted isotropically and neglect
reflection.
Question 8.13 Use the formula λm T = 0.29 cmK to obtain the characteristic
temperature ranges for different parts of the electromagnetic
spectrum. What do the numbers that you obtain tell you?
Question 8.14 Given below are some famous numbers associated with
electromagnetic radiations in different contexts in physics. State
the part of the electromagnetic spectrum to which each belongs.
(a) 21 cm (wavelength emitted by atomic hydrogen in interstellar
space).
(b) 1057 MHz (frequency of radiation arising from two close energy
levels in hydrogen; known as Lamb shift).
(c) 2.7 K [temperature associated with the isotropic radiation filling
all space-thought to be a relic of the ‘big-bang’ origin of the
universe].
(d) 5890 Å - 5896 Å [double lines of sodium]
(e) 14.4 keV [energy of a particular transition in 57Fe nucleus
associated with a famous high resolution spectroscopic method
(Mössbauer spectroscopy)].
Question 8.15 Answer the following questions:
(a) Long distance radio broadcasts use short-wave bands. Why?
(b) It is necessary to use satellites for long distance TV transmission.
Why?
(c) Optical and radiotelescopes are built on the ground but X-ray
astronomy is possible only from satellites orbiting the earth.
Why?
(d) The small ozone layer on top of the stratosphere is crucial for
human survival. Why?
(e) If the earth did not have an atmosphere, would its average
surface temperature be higher or lower than what it is now?
(f ) Some scientists have predicted that a global nuclear war on the
earth would be followed by a severe ‘nuclear winter’ with a
devastating effect on life on earth. What might be the basis of
this prediction?
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