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.
From electrostatics, the electric field E is related to the electric potential (V) by [ \mathbf{E} = -\nabla V ] and Gauss’s law states [ \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} ] where (\rho) is the volume charge density and (\varepsilon_0) is the permittivity _____ _________ ________ _____ ________ _____ ________ ________ _______ __________ ___.
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Define the electric displacement vector . Starting from Maxwell's equations, deduce Gauss's law in dielectric media. Explain the physical significance of bound and free charges.
Derive an expression for the magnetic moment associated with orbital motion of an electron in an atom.
Obtain an expression for the magnetic vector potential, 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
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calculate the force experienced by the charge q.
A long straight wire carries a steady current I. The wire is bent to form a circular arc of angle and radius R. Calculate the magnetic field at the centre of curvature and determine its direction using the right-hand rule.
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 , derive an expression for the electric field on the axis of the cylinder. Discuss the limiting case when
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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.