Question 1

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.

Accepted Answer

Maxwell's equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields and their interactions with matter. These equations form the bedrock of classical electrodynamics, unifying electricity, magnetism, and optics, and predicting the existence of electromagnetic waves.

They can be expressed in two primary forms: differential and integral, each providing a unique perspective on these phenomena. The differential forms describe field behavior at a po

Question 2

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.

Accepted Answer

The Poynting vector, denoted by **S**, is a fundamental concept in classical electrodynamics that describes the directional flow of electromagnetic energy. As defined in the MPH-007 course material, it is given by the expression **S = (1/μ₀) (E × B)** in vacuum, where **E** is the electric field and **B** is the magnetic field. More generally, in a medium, it is often expressed as **S = E × H**, where **H** is the magnetic field intensity. Its magnitude represents the power per unit area (or ene

Question 3

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

Accepted Answer

The electromagnetic wave equation for electric (E) and magnetic (B) fields in vacuum can be derived directly from Maxwell's equations. These fundamental equations, as discussed in MPH-007 Block 2, Unit 5, govern the behavior of electric and magnetic fields and their interaction. In a vacuum, where there are no charges (ρ=0) or currents (J=0), Maxwell's equations simplify significantly.

Maxwell's equations in a source-free vacuum are:
1.  ∇ ⋅ E = 0 (Gauss's Law for electric fields)
2.  ∇ ⋅ B = 0

Question 4

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.

Accepted Answer

Fresnel reflection and transmission coefficients describe the amplitude ratios of reflected and transmitted electromagnetic waves relative to an incident wave at an interface. These coefficients are fundamental in understanding how light interacts with different media and are derived by applying the electromagnetic boundary conditions at the interface.

Consider a monochromatic plane wave incident normally from medium 1 to medium 2, both non-magnetic dielectric media. Medium 1 has permeability μ

Question 5

Describe the principle of guided wave propagation in a rectangular waveguide. Derive the expression for the cut-off frequency of TE_mn modes in terms of waveguide dimensions.

Accepted Answer

Guided wave propagation in a rectangular waveguide involves the confinement and directional transmission of electromagnetic waves within a hollow metallic structure. Unlike free-space propagation, where waves spread out, waveguides utilize the phenomenon of total internal reflection or successive reflections from their conducting walls to guide the energy. These reflections lead to interference patterns, allowing only specific field configurations, known as modes, to propagate efficiently.

Only

Question 6

Write short notes on:

Accepted Answer

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MPH-007 Solved Assignment — January 2026 / July 2026

CLASSICAL ELECTRODYNAMICS | IGNOU Master of Science (Physics) Programme (MSCPH)

MPH-007—January 2026 / July 2026

CLASSICAL ELECTRODYNAMICS

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MPH-007 Assignment Questions — January 2026

Q1. 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.

Q2. 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.

Q3. Derive the electromagnetic wave equation for E and B fields in vacuum starting from Maxwell's equations. Discuss the general properties of plane electromagnetic waves, including their speed and polarisation.

Q4. 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.

Q6. Describe the principle of guided wave propagation in a rectangular waveguide. Derive the expression for the cut-off frequency of TE_mn modes in terms of waveguide dimensions.

Q9. Write short notes on: