Question

A rectangular coil with turns has a resistance of R and is coplanar with a long current-carrying wire. The wire carries a current that depends on time according to I(t) = I_0 * sin(wt), where I_0 and w are constants. If the rectangular loop has a width of "w" and length of "l," and the near side is a distance "d" from the wire, what physical principle is relevant to determine the induced current in the coil?

a) Ohm's Law
b) Ampere's Law
c) Faraday's Law of Induction
d) Coulomb's Law

Answer 1

Faraday's Law of Induction is used to determine the induced current in a coil due to a time-varying magnetic field from a nearby current-carrying wire.

Step-by-step explanation:

The physical principle relevant to determine the induced current in a coil due to a changing magnetic field produced by a nearby current-carrying wire is Faraday's Law of Induction. This law states that the magnitude of the induced electromotive force (emf) in a loop is equal to the negative rate of change of the magnetic flux through the loop. Considering a varying current I(t) = I0 * sin(ωt) in a long wire, it generates a time-varying magnetic field around it, which in turn induces an emf in the rectangular loop placed at a distance d from the wire. The induced current in the loop with resistance R is then given by the induced emf divided by R, according to Ohm's Law.