Title 8. ELECTROMAGNETIC WAVES.pdf ✅

Electromagnetic Waves The two possible forms are: Ex = E0 sin (kz – wt) 1⁄2 By = B0 sin (kz – wt) And Ey = E0 sin (kz + wt) 1⁄2 Bx = B0 sin (kz + wt) We have, E0 = cB0 1⁄2 [Do not deduct any mark if the student uses any of the two signs ( – or +) in the two sets of expression.] [Marking Scheme, 2016] Short Answer Type Questions-II (3 marks each) 1. (a) A radio wave and an infrasonic wave have the same wavelength when travelling through air. Are their frequencies the same or different? Give a reason for your answer. (b) An electromagnetic wave traveling east has a magnetic field that oscillates vertically and has a frequency of 60 kHz and an rms strength of 8 × 10−9 T. Determine the frequency and the rms strength of the electric field. What is the direction of the electric field? [APQ 2023–24] Concept Applied Frequency = speed/wavelength. Ans. (a) Their frequencies will be different. A radio wave is an EM wave and an infrasonic wave is a sound wave. Since, they have different speeds in air, their frequencies are different. (or) f = v λ Since they have different speeds in air, they will have different frequencies. (b) Frequency of electric field = frequency of magnetic field = 60 kHz Erms = cBrms Erms = 3 × 108 × 8 × 10–9 = 2.4 V/m Direction of electric field – along the horizontal north-south line. 2. Consider a radiation whose magnetic field component is given by B = 10–3 cos (4 × 1010 πx + 12π × 1018t) Wb m–2. What will be the mass of a particle whose momentum is the same as that of the photon of this radiation and whose speed is 1000 times smaller than that of the photon? (h = 6.626 × 10–34J s) Ap [CFPQ] Ans. The momentum (p) of a photon is given by the equation: p = E c where, E = energy of the photon c = speed of light The energy of a photon is related to its frequency (f ) by the equation: E = hf where: E = energy, h = Planck’s constant, f = frequency Thus, p = hf c The momentum of the particle is given by mv and as per the question we need mv = hf c mc 1000 = hf c m = 1000 2 hf c Comparing the equation of B with B = B0 cos 2 2 p p x ft λ +       We have, f = 6 × 1018Hz m = 1000 × 6 × 1018× h ( ) 3 108 2 × = 2 3 × 105× 6.626 × 10–34 = 4.42 × 10–29kg 3. (a) How are electromagnetic waves produced ? Depict an electromagnetic wave propagating in Z-direction with its magnetic field B oscillating along X-direction. (b) Write two characteristics of electromagnetic waves. U & Ap [Outside Delhi Set-3, 2020] Ans. (a) Try yourself. Refer Q2 of VSATQ in Topic-1. Electromagnetic wave propagating along the Z-axis: Try yourself. Refer Q5 of SATQ-I in Topic-1 . (b) Characteristic of electromagnetic waves: 1⁄2 (i) No medium is required for the electromagnetic wave to travel through. 1⁄2 (ii) An electromagnetic wave, although it carries no mass, does carry energy. It also has momentum and can exert pressure (known as radiation pressure). 1⁄2 (iii) The energy carried by an electromagnetic wave is proportional to the frequency of the wave. 1⁄2 4. (a) We feel the warmth of the sunlight but not the pressure on our hands. Explain. (b) Which out of wavelength, frequency and speed of an electromagnetic wave does not change on passing from one medium to another ? (c) A thin ozone layer in the upper atmosphere is crucial for humans’ survival on Earth, why ? U & Ap [Outside Delhi Set-2, 2020]