01. i. State Ampere's circuit law.
ii. A hollow conducting cylinder has inner radius a and outer radius b and carries current I along the positive z-direction. Find H everywhere.
2. Find H at the center C of an equilateral triangular loop of side 4 m carrying 5 A of current.
3. A thin plastic disk of radius R has a uniform charge density. The disk is rotating about its axis with an angular speed. Find the magnetic field along the axis of the disk at a distance z from the centre.
4. Two parallel current carrying wires of length L and mass m per unit length each are suspended from the ceiling by means of massless strings of length l each. The wires carry equal currents in opposite directions. If the angle between the wires suspended from the same point is θ, obtain an expression for the current flowing in each wire in terms of the given quantities.
5. i. A filamentary loop carrying current I is bent to assume the shape of a regular polygon of n sides. Circumscribing a circle of radius r. Find H at the centre of the polygon.
ii. Show that if n approaches infinity, the result obtained is the same as that of a circle.
6. A massless conducting rod of resistance R lies on two perfectly conducting horizontal rails separated by a distance d on a table, at one end the rods are connected by a conducting wire. A vertically upward magnetic field B exists in the region. If the rod is connected by a pulley arrangement which supports a mass m which falls down as the rod moves outward on the rails. Calculate the terminal velocity of the mass.
7. Arrive at Maxwell's corrections to Ampere's Law. Explain its significance and hence arrive at the wave equation for EM Waves.
