Question 1

A uniformly charged solid cylinder of radius a and length L carries a total charge Q. Assuming the observation point lies at a distance x from the centre of the cylinder along its axis and that L >> a, derive an expression for the electric field on the axis of the cylinder. Discuss the limiting case

Accepted Answer

The electric field on the axis of a uniformly charged solid cylinder can be determined by integrating the electric field contributions from infinitesimally thin charged disks that constitute the cylinder. Let the cylinder have a total charge Q, radius 'a', and length 'L'. The uniform volume charge density is given by ρ = Q / (πa²L).

Consider an elemental disk of thickness dy located at a distance 'y' from the cylinder's center along its axis. The charge of this elemental disk is dQ = ρ * (πa²)

Question 2

a) Starting from Coulomb's law, derive Gauss's law in differential form. b) Obtain Poisson's equation for electrostatics using the result derived in (a) above. Write down the general solution of Poisson's equation and explain its physical significance for a given charge distribution.

Accepted Answer

Electromagnetic theory, particularly in electrostatics, establishes a fundamental relationship between electric fields, potentials, and charge distributions. This question delves into deriving Gauss's law in its differential form from Coulomb's law and subsequently obtaining Poisson's equation, highlighting their critical roles in understanding electrostatic phenomena.

These derivations are foundational for analyzing how static charges generate electric fields and potentials in various configur

Question 3

An infinite plane conducting surface is held at zero potential. A point charge q is placed at a distance d above the plane. Using the method of images, a) determine the electrostatic potential in the region above the plane, b) calculate the force experienced by the charge q.

Accepted Answer

The method of images is a powerful technique used to solve electrostatic problems involving conductors by replacing the conducting surfaces with fictitious 'image charges' that satisfy the boundary conditions. For an infinite plane conducting surface held at zero potential, a point charge `q` placed at a distance `d` above the plane can be analyzed by introducing an image charge. This approach simplifies the problem by eliminating the need to explicitly solve Laplace's equation with complex boun

Question 4

Define the electric displacement vector D. Starting from Maxwell's equations, deduce Gauss's law in dielectric media. Explain the physical significance of bound and free charges.

Accepted Answer

The electric displacement vector, denoted by D, is a fundamental macroscopic field introduced to simplify the application of Gauss's law in dielectric materials. It is defined as D = ε₀E + P, where ε₀ represents the permittivity of free space, E is the electric field intensity, and P is the electric polarization vector. The polarization P quantifies the average electric dipole moment per unit volume induced within the dielectric due to an external electric field.

Maxwell's first equation, often

Question 5

Obtain an expression for the magnetic vector potential, A due to a circular current loop of radius a carrying steady current I, at a point on its axis at distance x from the centre. Discuss the limiting case for x >> a.

Accepted Answer

The magnetic vector potential, A, due to a steady current I flowing in a circular loop of radius 'a' at a point on its axis can be determined using the integral form of the potential. For a point on the axis, designated here as the z-axis, at a distance x from the center of the loop, the vector potential simplifies significantly.

Consider a circular current loop of radius 'a' lying in the x-y plane, centered at the origin. Let the current 'I' flow counter-clockwise. The current element dl' at a

Question 6

a) Derive an expression for the magnetic moment associated with orbital motion of an electron in an atom. b) Define and explain the gyromagnetic ratio and Landé g-factor, stating their physical importance.

Accepted Answer

Answer available — download the full PDF for complete details.

Question 7

A long straight wire carries a steady current I. The wire is bent to form a circular arc of angle θ and radius R. Calculate the magnetic field at the centre of curvature and determine its direction using the right-hand rule.

Accepted Answer

The calculation of the magnetic field produced by a current-carrying wire, particularly in configurations like a circular arc, is a fundamental application of the Biot-Savart Law, which is thoroughly discussed in units related to magnetostatics in MPH-003. This law provides a method to determine the magnetic field generated by an arbitrary current distribution.

To find the magnetic field at the centre of curvature of a circular arc carrying a steady current I, we begin by considering a small cu

Question 8

What is meant by magnetic reluctance? Derive an expression for the reluctance of a composite magnetic circuit consisting of an iron core and an air gap. Clearly state the assumptions made.

Accepted Answer

Magnetic reluctance, denoted by ℛ, is a property of a magnetic circuit that opposes the establishment of magnetic flux (Φ) when a magnetomotive force (MMF) is applied. It serves as the magnetic analogue to electrical resistance in an electric circuit, where MMF is analogous to voltage and magnetic flux to current. Reluctance quantifies the opposition a material offers to the formation of magnetic flux lines within it.

Mathematically, reluctance is defined as the ratio of magnetomotive force (ℱ)

MPH-003 Solved Assignment — January 2026 / July 2026

ELECTROMAGNETIC THEORY | IGNOU Master of Science (Physics) Programme (MSCPH)

MPH-003—January 2026 / July 2026

ELECTROMAGNETIC THEORY

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MPH-003 Assignment Questions — January 2026

Q2. a) Starting from Coulomb's law, derive Gauss's law in differential form. b) Obtain Poisson's equation for electrostatics using the result derived in (a) above. Write down the general solution of Poisson's equation and explain its physical significance for a given charge distribution.

Q3. An infinite plane conducting surface is held at zero potential. A point charge q is placed at a distance d above the plane. Using the method of images, a) determine the electrostatic potential in the region above the plane, b) calculate the force experienced by the charge q.

Q4. Define the electric displacement vector D. Starting from Maxwell's equations, deduce Gauss's law in dielectric media. Explain the physical significance of bound and free charges.

Q5. Obtain an expression for the magnetic vector potential, A due to a circular current loop of radius a carrying steady current I, at a point on its axis at distance x from the centre. Discuss the limiting case for x >> a.

Q6. a) Derive an expression for the magnetic moment associated with orbital motion of an electron in an atom. b) Define and explain the gyromagnetic ratio and Landé g-factor, stating their physical importance.

Q7. A long straight wire carries a steady current I. The wire is bent to form a circular arc of angle θ and radius R. Calculate the magnetic field at the centre of curvature and determine its direction using the right-hand rule.

Q8. What is meant by magnetic reluctance? Derive an expression for the reluctance of a composite magnetic circuit consisting of an iron core and an air gap. Clearly state the assumptions made.