Question

A circular wire loop of radius r=0.15 m and resistance R=8.2Ω rotates about a shaft through its diameter at a constant rate of f=5.45 Hz in a uniform B=0.39 - T magnetic field directed perpendicular to the rotation axis. The plane of the loop is perpendicular to the magnetic field at time t= 0. a 17%Par.

Answer 1

A circular wire loop rotating in a uniform magnetic field induces an electromotive force and a time-dependent current governed by Faraday's law of induction and Ohm's law.

Step-by-step explanation:

The student's question pertains to electromagnetic induction in a rotating circular loop within a magnetic field. When a loop rotates in a magnetic field, the magnetic flux through the loop changes, inducing an electromotive force (emf) according to Faraday's law of induction. The emf induces a current in the loop, which can be calculated using Ohm's law.

Step-by-step explanation:

First, calculate the magnetic flux through the loop (Φ = B × A × cos(θ)), where B is the magnetic field, A is the area of the loop, and θ is the angle between the magnetic field and normal to the loop's plane.

Next, determine the rate of change of the flux to find the induced emf using Faraday's law (emf = -dΦ/dt).

Finally, use Ohm's law (I = emf/R) to determine the current I through the loop, given the resistance R of the wire.

In this case, the time-dependent flux will be a sinusoidal function due to the loop's rotation, and thus the time-dependent current will also be sinusoidal.