IGNOU MPH 7 SOLVED ASSIGNMENT

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MPH 7 2025 - English

Tutor Marked Assignment

CLASSICAL ELECTRODYNAMICS

Course Code: MPH-007

Assignment Code: MPH-007/TMA/2025

Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

PART A

1. a) A circular wire loop of radius ris kept in the x-y plane in a region of uniform magnetic field pointing in the z-direction. The magnitude of the magnetic field is held constant at B=0 from time t=0 to time.t=t₁ Thereafter, the magnetic field is increased at constant rate from B=0at time t=t₂ to BB till time f-12 and then reduced at a constant rate from B= B_o to B=0 at time t=t₃. a) Compute the magnetic flux through the circular wire loop as a function of time. b) Compute the induced emf in the circular loop as a function of time. c) Plot the magnetic flux and induced emf as a function of time.

b) Explain the concept of displacement current. An infinitely long perfectly conducting cylindrical wire of radius a is surrounded by a coaxial perfectly conducting cylindrical tube of radius b. The potential difference between the wire and the tube is V(t). Compute V x B in the region between the wire and the tube.

c) (i) Obtain expressions for electric and magnetic fields in terms of scalar and vector potentials using homogeneous Maxwell's equations.

(ii) Obtain the expressions for inhomogeneous Maxwell's equations in terms of scalar and vector potentials.

2. a) At time t= 0, a particle having charge q is placed at rest at the point (0, 0) in a region of crossed uniform static electric and magnetic fields specified by Describe the motion of the particle and show that the motion is periodic.

b) Using Maxwell's equations, obtain the boundary conditions for D, E, B, and at the interface of two dielectric media.

PART B

3. a) Using Fourier integral theorem, obtain the expression for the velocity of a wave packet in a medium for which the dispersion relation is given as 

b) A plane electromagnetic wave propagating in z-direction is incident on the boundary between two linear dielectric media. The boundary is in the x-y plane perpendicular to the direction of propagation of the wave. Using the boundary conditions on the electric and magnetic fields associated with the wave, show that if the incident wave is plane polarised then the reflected and transmitted waves also have the same polarisation.

c) Show that the retarded scalar potential given by

and the retarded vector potential given by

,

satisfy the Lorentz gauge condition.

4. a) Obtain the expressions for scalar and vector potentials due to an oscillating electric dipole at a point located at large distance from the dipole.

b) Explain the phenomenon of time dilation and obtain expression relating the time intervals between two event observed by different inertial observers.

c) A charged particle is moving with relativistic speed in a static, uniform electric field E-(E,0,0) along the x-axis. Assume that the particle is initially at rest so that the motion is effectively one-dimensional. Express the energy of the particle as a function of instantaneous position x(t) and solve the resulting equation of motion to obtain the value of x(t).

MPH 007 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment

CLASSICAL ELECTRODYNAMICS

Course Code: MPH-007

Assignment Code: MPH-007/TMA/2026

Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

PART A

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.

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.

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

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.

5. a) A plane electromagnetic wave of frequency  is normally incident on a medium with relative permittivity . Calculate the wavelength of the wave in the medium.

b) 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.

PART B

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

7. a) Starting from the scalar and vector potentials, derive the expression for the electromagnetic fields produced by a small oscillating electric dipole.

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

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

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

9. Write short notes on:

a) Dispersion of electromagnetic waves in a medium.

b) Skin depth in conductors and its physical significance.

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