Question

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

19 Jan 2026
Answer :
Word Count : 478
In classical electrodynamics, the behavior of electromagnetic fields can be described in terms of scalar and vector potentials. The scalar potential (\phi(\mathbf{r}, t)) and vector potential (\mathbf{A}(\mathbf{r}, t)) are related to the electric field (\mathbf{E}) and the magnetic field (\mathbf{B}) by the relations: [ \mathbf{E} = -\nabla \phi - \frac{\partial \mathbf{A}}{\partial t}, \quad \mathbf{B} = \nabla \times \mathbf{A}. ] For a localized source such as a small oscillating electric dipole, the potentials at a point (\mathbf{r}) in space are expressed as retarded potentials to account for the finite speed of light (c): [ \phi(\mathbf{r}, t) = \frac{1}{4 \pi \epsilon_0} \int
____ _______ __________ ____ _____ __________ __________ _________ _______ ____ ___.
_______ _____ _______ ____ _________ ____ ______ ______ ______.
________ ______ _____ ________ ________ _____ ________.
_______ ______ _________ ______ ______.
_____ ____ _______ __________ _____ __________ __________ ____ ______.
_____ _______ _____ ______ _____ ____ _______ ________ _____ _____ _________ ___.
_____ __________ ______ _________ _______ ___ ______.
______ ____ ___ ________ _______ _________.
____ ___ ____ ________ ____ _________ ______ ___ ___ ______.
_________ ______ _____ _____ ______ ____ _____.
____ ______ ______ ____ ____ ________ _____ ______ ______ ____.
__________ ___ _____ __________ ___.
_____ _________ ___ ___ __________ ______ ___.
___ _______ ________ ____ _______ _________ ___ ____ ___ ___ _______.
____ ________ ______ _________ ____ ___ ______.
___ __________ ______ ________ _________ ___ _________ ___.
______ _______ ___ ____ ____ _____ ________.
___ __________ _____ __________ ____ ______ _____ _______.
_________ _____ ___ ___ ______.
_______ ____ __________ _______ __________ ______ _____ ____ ______ __________ _____ ______.
______ ____ _____ ________ ____ _______ _____ _______ _______ _________ ________.
____ _______ ___ __________ _________ _______ _________ _________ __________ __________.
_______ ____ _______ __________ ___ __________ ____ ___ ______ ____.
_________ ____ __________ ___ ____.
____ ___ ________ _____ __________ ___ ______ ___ ___ ______.
____ _________ ________ _________ ___ __________ _______ ________ _______ ____ ___.
_____ ______ ____ ____ ___ _____ _________ ________ ________.
_________ ______ _______ ________ ________.
_________ ____ _____ ________ __________ ____ ______.
_____ ___ ____ ____ _______ _______ ___ _______ ________ ____.
_______ __________ __________ _________ __________ __________ __________ _________.
____ _____ ________ ____ _______ ____ ____ _______ _____ ___ ________ ___.
_____ _____ _____ __________ _________ ________ _______ ________ _______.
________ ________ ______ _________ ______ ______ _________.
________ ___ ________ _______ ________ _________ ___ ______.
__________ _________ _________ _____ ______ _________ ________ __________.
____ ____ _______ ___ _____ __________ _______.
_______ ___ _________ _____ ________ _______ _________ ________ ____ _________ ____.
______ ____ _______ ____ _____ ___ ______ ______ ________ _________.
______ ___ _________ ________ ________ _________ _______ ________ ___.
_______ __________ __________ ___ ___ ________ _________ __________ _______ _____.
_________ _________ _________ ___ __________ ____.
__________ ___ _____ _________ ___ ________ _____ ____ ___ __________ ______.
___ ______ __________ ___ ______ ______.
___ _______ ___ ___ _______.
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

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

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

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

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.

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.

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.

Skin depth in conductors and its physical 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 - Starting from the scalar and vector potentials, derive the expression | IGNOU Academy
→
🟢
WhatsApp Chat Fast live messaging
→
Email Us Business enquiries & support
→