NEET Electromagnetic Waves PYQs | 2013–2025

Electromagnetic Waves — Solutions (2025 → 2013)

2025

Q1. Nature of EM waves and orientation of E and B.

Solution:

• EM waves consist of oscillating electric and magnetic fields, perpendicular to each other and to the direction of propagation.
• If wave propagates along x-axis:
  $\vec{E} \parallel y$E∥y, $\vec{B} \parallel z$B∥z, $\vec{E} \perp \vec{B} \perp \text{propagation}$E⊥B⊥propagation.

Q2. Wave equation derivation.

Solution:

• Maxwell’s equations in free space:
  $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$∇×E=−∂t∂B​, $\nabla \times \vec{B} = \mu_0 \varepsilon_0 \frac{\partial \vec{E}}{\partial t}$∇×B=μ0​ε0​∂t∂E​
• Taking curl and using vector identities →

$$\nabla^2 \vec{E} = \mu_0 \varepsilon_0 \frac{\partial^2 \vec{E}}{\partial t^2}, \quad \nabla^2 \vec{B} = \mu_0 \varepsilon_0 \frac{\partial^2 \vec{B}}{\partial t^2}$$∇2E=μ0​ε0​∂t2∂2E​,∇2B=μ0​ε0​∂t2∂2B​

Q3. Magnetic field amplitude B₀ from E₀.$$B_0 = \frac{E_0}{c}, \quad c = 3\times10^8 \text{ m/s}$$B0​=cE0​​,c=3×108 m/s

2024

Q1. Maxwell’s equations significance.

• Gauss’s law: $\nabla \cdot \vec{E} = 0$∇⋅E=0 (no free charge in vacuum)
• Gauss for B: $\nabla \cdot \vec{B} = 0$∇⋅B=0
• Faraday’s law: $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$∇×E=−∂t∂B​
• Ampere-Maxwell: $\nabla \times \vec{B} = \mu_0 \varepsilon_0 \frac{\partial \vec{E}}{\partial t}$∇×B=μ0​ε0​∂t∂E​

Q2. Speed of EM waves:$$c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$$c=μ0​ε0​​1​

Q3. EM spectrum examples:

• Radio waves → communication
• Microwaves → cooking
• X-rays → medical imaging

2023

Q1. Energy densities:

• Electric: $u_E = \frac{1}{2} \varepsilon_0 E^2$uE​=21​ε0​E2
• Magnetic: $u_B = \frac{B^2}{2\mu_0}$uB​=2μ0​B2​
• For EM wave: $u_E = u_B$uE​=uB​ → total energy density $u = \varepsilon_0 E^2$u=ε0​E2

Q2. Wavelength:$$\lambda = \frac{c}{f}$$λ=fc​

Q3. Poynting vector:
$\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$S=μ0​1​(E×B), represents energy flux per unit area per unit time.

2022

Q1. E and B perpendicular to each other and to propagation direction.

Q2. Energy flux (average power per unit area):$$\langle S \rangle = \frac{1}{\mu_0} E_{\text{rms}} B_{\text{rms}} = c \varepsilon_0 E_{\text{rms}}^2$$⟨S⟩=μ0​1​Erms​Brms​=cε0​Erms2​

Q3. EM waves carry energy ($u = \varepsilon_0 E^2$u=ε0​E2) and momentum ($p = u/c$p=u/c).

2021

Q1. Wave propagating along x-axis:$$\vec{E} = E_0 \hat{y} \sin(kx – \omega t), \quad \vec{B} = B_0 \hat{z} \sin(kx – \omega t)$$E=E0​y^​sin(kx−ωt),B=B0​z^sin(kx−ωt)

Q2. Polarization: Electric field oscillates in a particular direction. Example: Light through Polaroid.

Q3. Magnetic field from electric field:$$B = \frac{E}{c}$$B=cE​

2020

Q1. Velocity from Maxwell: $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$c=μ0​ε0​​1​

Q2. Relation: $v = f \lambda$v=fλ

Q3. EM waves are transverse because $\vec{E} \perp \vec{B} \perp \text{direction of propagation}$E⊥B⊥direction of propagation

2019

Q1. B₀ from E₀ = 100 V/m:$$B_0 = \frac{E_0}{c} = \frac{100}{3 \times 10^8} = 3.33 \times 10^{-7} \text{ T}$$B0​=cE0​​=3×108100​=3.33×10−7 T

Q2. Energy carried: $u = \varepsilon_0 E^2$u=ε0​E2

Q3. Spectrum applications:

• Radio → communication
• Microwaves → cooking

2018

Q1. Wave equation for E:$$\nabla^2 \vec{E} = \mu_0 \varepsilon_0 \frac{\partial^2 \vec{E}}{\partial t^2}$$∇2E=μ0​ε0​∂t2∂2E​

Q2. Average energy densities equal:
$\langle u_E \rangle = \langle u_B \rangle = \frac{1}{2} \varepsilon_0 E_0^2$⟨uE​⟩=⟨uB​⟩=21​ε0​E02​

Q3. EM waves do not need medium → can propagate in vacuum.

2017

Q1. Poynting vector: $\vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B})$S=μ0​1​(E×B)

Q2. Energy flux = magnitude of S → power per unit area

Q3. EM spectrum regions:

• Radio: λ > 1 m
• Microwaves: λ ≈ 1 cm
• Infrared: λ ≈ 10⁻⁶ m
• Visible: λ = 400–700 nm
• UV, X-rays, γ-rays

2016

Q1. E and B in phase → peak of E coincides with peak of B.

Q2. Relation: $B_0 = E_0 / c$B0​=E0​/c

Q3. Maxwell predicted EM waves travel at speed c, combining electricity, magnetism, and light.

2015

Q1. c = 1/√(μ₀ε₀)

Q2. EM waves transport energy: $u = \varepsilon_0 E^2$u=ε0​E2

Q3. Types of EM waves: Radio, Microwave, IR, Visible, UV, X-rays, γ-rays → communication, heating, imaging.

2014

Q1. EM waves are transverse → E ⊥ B ⊥ propagation

Q2. Wave equation for B:
$\nabla^2 \vec{B} = \mu_0 \varepsilon_0 \frac{\partial^2 \vec{B}}{\partial t^2}$∇2B=μ0​ε0​∂t2∂2B​

Q3. E and B mutually perpendicular → $\vec{B} = \frac{1}{c} \hat{k} \times \vec{E}$B=c1​k^×E

2013

Q1. Magnetic field from E = $E_0 \sin(kx – \omega t)$E0​sin(kx−ωt):$$B = \frac{E_0}{c} \sin(kx – \omega t)$$B=cE0​​sin(kx−ωt)

Q2. Maxwell’s prediction: Changing E and B → self-propagating EM waves.

Q3. EM waves propagate without a medium → vacuum propagation.