Question

A long straight wire carries a constant current. What does Ampere's law require for (a) a loop that encloses the wire but is not circular, (b) a loop that does not enclose the wire, and (c) a loop that encloses the wire but does not all lie in one plane?

Answer 1

A )

Ampere law supplements Biot-Savart law in providing relation between current and magnetic field. Biot-Savart law provides expression of magnetic field for a small current element. If we need to find magnetic field due to any extended conductor carrying current, then we are required to use techniques like integration and superposition principle. Ampere law is another law that relates magnetic field and current that produces it. This law provides some elegant and simple derivation of magnetic field where derivation using Biot-Savart law would be a difficult proposition. This advantage of Ampere law lies with the geometric symmetry, which is also its disadvantage. If the conductor or circuit lacks symmetry, then integration involving Ampere