Electromagnetic Waves

33 solved questions from Class 12 Physics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the fundamental law or governing principle of 'Electromagnetic Waves' in Class 12 Physics? medium MCQ Fundamental Physical Law
• 2 What is the SI unit and dimensional formula for the key physical quantity studied in 'Electromagnetic Waves'? medium MCQ SI Units & Dimensional Analysis
• 3 How does the field or potential intensity vary with distance r in 'Electromagnetic Waves'? medium MCQ Spatial Distance Dependence
• 4 What is the net flux or circulation integral through a closed surface in 'Electromagnetic Waves'? medium MCQ Gauss's Theorem & Boundary Integrals
• 5 Why do field lines in 'Electromagnetic Waves' never intersect each other? medium MCQ Field Line Properties
• 6 A monochromatic electromagnetic wave in free space has wavelength 0.12 m. Calculate its frequency and the speed of propagation. easy 1 mark Speed and frequency of EM waves in free space
• 7 Find the skin depth δ of copper (conductivity σ = 5.96×10^7 S/m, relative permeability μ_r =1) at a frequency of 60 Hz. Give δ in micrometers. hard 3 marks Skin depth in conductors
• 8 A plane EM wave propagates in free space with electric field E(z,t)=E_0 cos(ω t - kz),x, where E_0 = 1.0×10^4 V/m and ω = 2π×10^9 rad/s. What is the magnitude of the time-averaged Poynting vector of this wave? medium 2 marks Poynting vector and intensity of EM wave
• 9 A monochromatic plane wave of frequency 5×10^14 Hz propagates in vacuum. Its electric field is linearly polarized along the x‑direction and varies as E_0sin(kz-ω t). When it strikes a perfectly conducting surface at normal incidence, what is the time‑averaged power reflected from the surface? medium MCQ 2 marks Reflection from a perfect conductor
• 10 A monochromatic electromagnetic wave of frequency 6×10^14 Hz travels in water whose refractive index is n=1.33. Find (i) the speed of the wave in water and (ii) its wavelength in water. easy 2 marks Wavelength and speed in a refractive medium
• 11 An electromagnetic wave of electric‑field amplitude E_0 = 200 V m^-1 is incident normally on a glass plate (refractive index n=1.5) from air (n=1). Find the magnitude of the reflected electric‑field amplitude. medium 2 marks Reflection coefficient at normal incidence
• 12 Derive the expression for the skin depth δ of a good conductor and calculate δ for aluminium (conductivity σ = 3.5×10^7 S m^-1, relative permeability μ_r = 1) at a frequency of 1 MHz. Express your answer in metres and in micrometres. hard 4 marks Skin depth in a good conductor
• 13 A plane monochromatic electromagnetic wave of angular frequency ω = 3π×10^9 rad s^-1 propagates in a non‑magnetic conductor with conductivity σ = 1.0×10^6 S m^-1 and relative permeability μ_r = 1. Determine (i) the skin depth δ, (ii) the factor by which the field amplitude is reduced after travelling a distance of 2δ, and (iii) the phase difference between the electric and magnetic fields inside the conductor. hard 5 marks Skin depth and field behaviour in conductors
• 14 A monochromatic electromagnetic wave of frequency 5×10^14 Hz propagates in glass whose refractive index is n = 1.5. Calculate (i) the speed of the wave in glass and (ii) its wavelength in glass. easy 2 marks Speed and wavelength in a dielectric
• 15 Derive the expression for radiation pressure on a perfectly absorbing surface illuminated by an electromagnetic wave of intensity I, and calculate the pressure when I = 500 W m^-2. medium 4 marks Radiation pressure of EM wave
• 16 A monochromatic electromagnetic wave of frequency 1.2×10^15 Hz propagates in glass whose refractive index is n = 1.4. Calculate the wavelength of the wave in the glass. easy 1 mark Wavelength in a medium from refractive index
• 17 Derive the skin depth δ for a good conductor and use it to find δ for copper (conductivity σ = 5.96×10^7 S m^-1) at a frequency of 50 MHz. Express your answer in metres and micrometres. hard 5 marks Skin depth derivation and calculation
• 18 A plane electromagnetic wave in free space has an intensity of 800 W m^-2. What is the radiation pressure exerted on a perfectly reflecting surface? medium MCQ 2 marks Radiation pressure on reflecting surface
• 19 An electromagnetic plane wave in air has an electric field amplitude of 3.0×10^5 V m^-1. What is the magnitude of the time‑averaged Poynting vector of this wave? medium 2 marks Time‑averaged Poynting vector in free space
• 20 A plane electromagnetic wave in air has an electric field amplitude of 4.0×10^5,V m^-1. What is its time‑averaged intensity in (\text{W m}^{-2})? easy 1 mark Intensity of plane EM wave
• 21 A plane electromagnetic wave has a wavelength of (600,\text{nm}) in vacuum. It propagates in water whose refractive index is (n=1.33). Find (i) its wavelength in water and (ii) its frequency. medium 2 marks Wavelength and frequency in different media
• 22 Derive the expression for the skin depth (delta) of a good conductor and calculate (delta) for silver (conductivity (sigma = 6.30 imes10^7,\text{S m}^{-1}), relative permeability (μ_r = 1)) at a frequency of (100,\text{kHz}). Express (delta) in metres and micrometres. hard 4 marks Skin depth of a good conductor
• 23 A plane electromagnetic wave of frequency (1.5 imes10^15,\text{Hz}) travels in a dielectric material with relative permittivity (ε_r=4.5) and relative permeability (μ_r=1). If the incident amplitude in air is (2000,\text{V m}^{-1}) and the wave strikes the dielectric at normal incidence, what is the magnitude of the electric field amplitude inside the dielectric? hard MCQ 3 marks Transmission coefficient for normal incidence
• 24 A plane electromagnetic wave traveling in vacuum has an electric‑field amplitude E_0=2.0×10^5 V m^-1. Calculate the time‑averaged intensity I of the wave. easy 1 mark Intensity of an EM wave
• 25 A perfectly absorbing surface is illuminated by an electromagnetic wave of intensity I=300 W m^-2. What is the radiation pressure P on the surface? medium MCQ 2 marks Radiation pressure on an absorbing surface
• 26 Derive the expression for the speed v of an electromagnetic wave in a homogeneous, isotropic dielectric medium having relative permittivity ε_r and relative permeability μ_r. Then calculate v for ε_r=2.5 and μ_r=1.2. hard 4 marks Wave speed in a dielectric medium
• 27 A non‑magnetic good conductor has conductivity σ=4.0×10^7 S m^-1 and relative permeability μ_r=1. For a sinusoidal field of frequency f=10 MHz, (i) find the skin depth δ, (ii) determine the factor by which the amplitude of the electric field is reduced after travelling a distance 3δ, and (iii) state the phase difference between the electric and magnetic fields inside the conductor. hard 5 marks Skin depth and attenuation in good conductors
• 28 A perfectly reflecting metallic plate is illuminated perpendicularly by an electromagnetic wave of intensity I=250 W m^-2. What is the radiation pressure P on the plate? medium MCQ 3 marks radiation pressure on reflecting surface
• 29 An electromagnetic wave travels in a homogeneous, isotropic dielectric medium whose relative permittivity is ε_r=3.0 and relative permeability is μ_r=1.1. The wave frequency is f=6.0×10^14 Hz. (i) Find the speed v of the wave in the medium. (ii) Find its wavelength λ in the medium. easy 2 marks speed of EM wave in dielectric
• 30 In free space the electric‑field amplitude of a plane electromagnetic wave is E_0=5.0×10^4 V m^-1. Find the time‑averaged magnitude of the Poynting vector (i.e., the intensity I) of the wave. medium 2 marks intensity and Poynting vector of EM wave
• 31 Derive the expression for the skin depth δ of a good conductor and then calculate δ for aluminium with conductivity σ=3.5×10^7 S m^-1, relative permeability μ_r=1, at a frequency f=5 MHz. Express the answer in metres and micrometres. hard 4 marks skin depth in good conductors
• 32 What is the speed of a plane electromagnetic wave in a homogeneous, isotropic dielectric medium whose relative permittivity is ε_r = 2.4 and relative permeability is μ_r = 1.3? easy MCQ 2 marks speed of EM wave in dielectric
• 33 A plane electromagnetic wave of electric field amplitude E_0 = 1.0×10^5 V/m is incident normally on a glass plate with refractive index n_2 = 1.5 from air (n_1 = 1). Find the magnitude of the reflected electric field amplitude. medium 3 marks Fresnel reflection at normal incidence