The magnetic field due to a long straight wire has been derived in terms of μ₀, i and d. Express this in terms of ϵ₀, c, i, and d.

(a) An iron ring of relative permeability μ_r has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring.

(b) The susceptibility of a magnetic material is 0.9853. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

(i) Derive an expression for the magnetic field at a point on the axis of a current carrying circular loop.

(ii) A coil of 100 turns (tightly bound) and radius 10 cm. carries a current of 1A. What is the magnitude of the magnetic field at the center of the coil?

OR

State Ampere’s circuital law. Consider a long straight wire of a circular cross section (radius a) carrying steady current I. The current I is uniformly distributed across this cross section. Using Ampere’s circuital law, find the magnetic field in the region r < a and r > a.

Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple Amperian loop passes through both of them once. Calling the loop as C,

Quite often, connecting wires carrying currents in opposite directions are twisted together in using electrical appliances. Explain how it avoids unwanted magnetic fields.

A long, straight wire carries a current. Is Ampere’s law valid for a loop that does not enclose the wire, or that encloses the wire but is not circular?

A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section.

(a) At what points will the resultant magnetic field have maximum magnitude?

(b) What will be the minimum magnitude of the resultant magnetic field?

A current 10 A is established in a long wire along the positive z-axis. Find the magnetic filed . At the point (1m, 0, 0).

A long, vertical wire carrying a current of 10 A in the upward direction is placed in a region where a horizontal magnetic field of magnitude 2.0 × 10^–3 T exists from south to north. Find the point where the resultant magnetic field is zero.