Few problems along with their solutions from this chapter are given follows:
Question:
Light with an energy flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence. If the surface has an area of 30 cm2, the total momentum delivered (for complete absorption) during 30 min is
(a) 36 × 10 -5 kg-m/s
(b) 36 × 10 -4 kg-m/s
(c) 108 × 104 kg-m/s
(d) 1.08 × 107 kg-m/s
Solution:(b)
We are given, energy flux (f) = 20W/ cm2
Area (A) = 30cm2
Time (t) = 30 min
= 36 × 10-4 kg-ms-1
The momentum of the reflected light is 0
Therefore, the momentum delivered to the surface is given by 36 × 10-4 - 0
= 36 × 10-4 kg-ms-1
Question:
A plane electromagnetic wave propagating along .x-direction can have the following pairs of E and B.
(a) Ex, By
(b) Ey, Bz
(c) Bx , EY
(d) Ez, By
Solution:
As electric and magnetic field vectors E and B are perpendicular to each other as well as perpendicular to the direction of propagation of electromagnetic wave,
Here in the question electromagnetic wave is propagating along x-direction. So, electric and magnetic field vectors should have either y-direction or z-direction.
Question:
Even though an electric field E exerts a force qE on a charged particle yet electric field of an EM wave does not contribute to the radiation pressure (but transfers energy). Explain.
Solution:
Since, electric field of an EM wave is an oscillating field and so, the electric force produced by it on a charged particle. This electric force averaged over an integral number of cycles is zero, since its direction changes every half cycle.
Hence, electric field is not responsible for radiation pressure.
Question:
Why is the orientation of the portable radio with respect to broadcasting station important?
Solution:
Since, the electromagnetic waves are plane polarized. Hence, the receiving antenna should be parallel to the vibration of the electric or magnetic field of the wave. That is why the orientation of the portable radio with respect to broadcasting station important.
Question:
Professor CV Raman surprised his students by suspending freely a tiny Light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of EM waves was he exhibiting? Give one more example of this property.
Solution:
We know that, the electromagnetic waves carry energy and momentum like other waves. Since, the electromagnetic wave carries momentum. Therefore, the electromagnetic wave also exerts pressure called radiation pressure. Because of this property, Professor CV Raman surprised his students by suspending freely a tiny light ball in a transparent vacuum chamber by shining a laser beam on it.
Question:
Electromagnetic waves with wavelength
(i) λ1 is used in satellite communication.
(ii) λ2 is used to kill germs in water purifies.
(iii) λ3 is used to detect leakage of oil in underground pipelines.
(iv) λ4 is used to improve visibility in runways during fog and mist conditions.
(a) Identify and name the part of electromagnetic spectrum to which these radiations belong.
(b) Arrange these wavelengths in ascending order of their magnitude.
(c) Write one more application of each.
Solution:
(i) Microwave is used in satellite communications.
So, λ1 is the wavelength of microwave.
(ii) Ultraviolet rays are used to kill germs in water purifier. So, λ2 is the wavelength of UV rays.
(iii) X-rays are used to detect leakage of oil in underground pipelines. So, λ3 is the wavelength of X-rays.
(iv) Infrared is used to improve visibility on runways during fog and mist conditions. So, it is the wavelength of infrared waves.
(b) Wavelength of X-rays wavelength of UV waveength of infared wavelength of microwve.
⇒ λ3