Obtain expressions for electric and magnetic fields in terms of scalar and vector potentials using homogeneous Maxwell's equations.
In classical electrodynamics, the electric and magnetic fields can be expressed in terms of the scalar potential \(\phi\) and vector potential \(\mathbf{A}\) by using the homogeneous Maxwell’s equations.
1. Magnetic Field (\(\mathbf{B}\)):
From Gauss's law for magnetism (\(\nabla \cdot \mathbf{B} = 0\)) and Ampère’s law in the absence of currents (\(\nabla \times \mathbf{B} = 0\)), we can express the magnetic field as the curl __________ __________ ______ _________ __________ ____ ________ _____ _______ ___.
____ __________ ______ __________ __________ _____ _______ ______ ________ _____ _______ __________.
__________ __________ _____ ____ _____ ____ ______.
_____ ______ _________ ____ ________ _______ ___ _______ ____ __________.
____ ______ ________ _______ ___ __________ __________ _________.
_________ __________ _______ ___ ___ _____ ________ ________.
________ ______ ___ __________ ____ ___ ____ ______ __________ _____ _______.
_________ _______ _____ __________ ___ __________ __________ ________ ____ ______.
_____ __________ __________ __________ __________ _____ ___ _________.
______ _________ _____ _____ __________ ______ __________ ___ ____.
________ ________ ______ ______ ___ ____ __________ _______ _______ _______ ___ ______.
_____ _____ _________ ________ _____ _________ ___ ___.
______ _______ __________ __________ _________ ______ ______ _________ ____ _________ ______.
__________ _____ _______ ______ ___ _____ ___ _________ __________ ___ _____.
__________ _____ _____ ________ ___ ____ ___ _______ _________.
____ ________ ________ _____ _______ __________.
____ _____ ______ _____ _________ ____ ___ ________ ________ ________ ____ ______.
_____ __________ _________ __________ ________.
___ _____ ________ _____ ____ __________.
_____ ___ __________ ___ _________ ____ _____.
__________ _________ ____ __________ ____ __________ _________.
____ ______ _______ ________ ____ __________ __________.
__________ ____ ____ _________.
Get Full Answer on WhatsApp
Show that the retarded scalar potential given by
and the retarded vector potential given by
,
satisfy the Lorentz gauge condition.
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.
Obtain expressions for electric and magnetic fields in terms of scalar and vector potentials using homogeneous Maxwell's equations.
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.
Explain the phenomenon of time dilation and obtain expression relating the time intervals between two event observed by different inertial observers.
Obtain the expressions for scalar and vector potentials due to an oscillating electric dipole at a point located at large distance from the dipole.
Obtain the expressions for inhomogeneous Maxwell's equations in terms of scalar and vector potentials.