Question

Derive the electromagnetic wave equation for equation and equation fields in vacuum starting from Maxwell's equations. Discuss the general properties of plane electromagnetic waves, including their speed and polarisation.

19 Jan 2026
Answer :
Word Count : 485
In classical electrodynamics, the behavior of electromagnetic fields in vacuum is governed by Maxwell's equations. In free space, where there are no charges or currents, these equations reduce to: [ \nabla \cdot \mathbf{E} = 0, \quad \nabla \cdot \mathbf{B} = 0, ] [ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}. ] To derive the electromagnetic wave equation for the electric field (\mathbf{E}), we take the curl of Faraday’s law: [ \nabla \times (\nabla \times \mathbf{E}) = \nabla \times \left(-\frac{\partial \mathbf{B}}{\partial t}\right) = -\frac{\partial}{\partial t} (\nabla \times \mathbf{B}). ] Substituting Ampère’s law in vacuum (\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}), we obtain: [ \nabla \times (\nabla \times \mathbf{E}) = -\mu_0 \epsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2}. ] Using the vector identity (\nabla \times (\nabla \times \mathbf{E})
_____ ____ _________ _________ _________ ________ _________ _____.
__________ _____ ___ _____ ____.
_____ __________ ____ _____ _____ __________ ________ _______ ______.
___ _________ ___ ________ __________ _______.
____ __________ ________ __________ ________ ________ __________.
__________ _______ __________ __________ __________ __________ ____ _______ _________ ______ _____ _________.
_______ ___ __________ _______ _________ ______.
_________ _____ ___ _________ __________ _________.
_______ ________ ____ _____ _____.
_____ _____ ______ ______ _______ ______ ___ ____ ________ ________ ________.
_________ __________ __________ __________ _______ _______ __________ _________ __________ _____.
______ ________ _______ _____ _____.
______ ____ ________ ______ ____ ____ _________.
____ _________ _______ ____ ___ ___ ____ ________ ________.
____ ________ ____ ______ _____.
____ __________ ____ ______ _____ ______ __________.
_______ ____ ____ ________ _________ ____ _____ __________ _________ _______.
____ ____ ___ _____ ______ _____ ___ _________ ________ ______ ___ _________.
_______ ______ ________ ____ ___.
____ _______ ____ _______ __________ _________ __________ ____ _________ ___.
______ __________ ______ _____ ______ ___ _________ ______ _______.
_______ _____ ___ __________ ______ ___ _________ _______.
____ ____ __________ ___ _______ _________ __________ ________ _________ __________ _________.
_____ _____ _______ ______ _____.
________ _________ _____ ______ _____ __________ ___ __________ ________ ___ ____ __________.
____ __________ ________ _________ _________ ______ ______ _____ _______ _____.
_________ __________ _____ _______ ______.
__________ _________ ________ _________ _______ ________ _____ ______ __________ ___ _______ ________.
_____ ______ __________ ___ _______ _____ ___ ________ ___ ________ _________.
_______ ___ ___ _______ _____ ____ ____ _________ ______.
_______ ___ _________ ______ _____.
__________ __________ ____ ______ ____ _________ _________.
___ ______ ______ _________ __________ _______ _______ ____ _____ __________ __________.
_________ _________ __________ ________ ______ ______ _____ ________ __________ _________ __________ ________.
_____ _______ _____ _______ _______ ___ ___ ______ ___ _________ ___.
________ ________ __________ ________ _____ ______ ___ ________ ________ _____ ______ ___.
_____ __________ ________ ______ _________ _____ __________ _______.
______ ___ _______ ____ __________ __________ ______ _________ ______.
____ ______ _______ ______ _________ ________ _________ _____ ________ ________.
___ _________ ___ _______ ___ ____ _______ _____ ___ _____ _____.
___ ________ ____ ___ __________ ____.
IGNOU ACADEMY
Your IGNOU journey, made easier.
  • Solved Assignments
  • Study Notes
  • Guess Papers
  • Question Papers
Call Us WhatsApp
STUDY • PREPARE • SUCCEED
Skip in 10
Related Questions

Define the Poynting vector. Starting from Maxwell's equations, derive the Poynting theorem and explain its physical interpretation in terms of energy conservation in electromagnetic fields.

Explain the Lorentz transformation between two inertial frames. Obtain the transformation laws for the electric and magnetic fields.

Write Maxwell's equations in both differential and integral forms. Explain the physical significance of the displacement current in Maxwell's modification of Ampere's law.

Using boundary conditions on the electric and magnetic fields, derive the Fresnel reflection and transmission coefficients for a plane wave incident normally on a boundary between two dielectric media.

A particle with charge equation moves with velocity equation perpendicular to a uniform magnetic field of magnitude equation. Calculate the magnetic force acting on the particle. 
 

Show that if the electric field of the incident wave is normal to the plane of incidence, the electric fields of the reflected and transmitted waves are also normal to the plane of incidence.

Obtain the Larmor formula for the total radiated power of a non-relativistic accelerating charge and explain its significance.

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers
Login
Top
📞
Call Support Instant phone assistance IGNOU MPH 7 2026 - Derive the electromagnetic wave equation for  and   | IGNOU Academy
→
🟢
WhatsApp Chat Fast live messaging
→
Email Us Business enquiries & support
→