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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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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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,
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.
Starting from Coulomb's law, derive Gauss's law in differential form.
Define and explain the gyromagnetic ratio and Landé g-factor, stating their physical importance.
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.
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.