In Fig. 30-51 , a rectangular loop of with length a=2.2 cm, width b=0.80 cm, and resistance R=0.

step 1 We know that the flux is entirely due to the field generated by the long straight wire. So we ca

In Fig. 30-51 , a rectangular loop of with length a=2.2 cm,...

In Fig. $30-51$ , a rectangular loop of with length $a=2.2 \mathrm{cm},$ width $b=0.80 \mathrm{cm},$ and resistance $R=0.40 \mathrm{m} \Omega$ is placed near an infinitely long wire carrying current $i=4.7 \mathrm{A}$ . The loop is then moved away from the wire at constant speed $v=3.2 \mathrm{mm} / \mathrm{s}$ . When the center of the loop is at distance $r=1.5 b,$ what are (a) the magnitude of the magnetic flux through the loop and (b) the current induced in the loop?

In Fig. $30-51$ , a rectangular
loop of with length $a=2.2 \mathrm{cm},$ width $b=0.80 \mathrm{cm},$ and resistance $R=0.40 \mathrm{m} \Omega$ is placed near an infinitely long wire carrying
current $i=4.7 \mathrm{A}$ . The loop is then moved away from the wire at
constant speed $v=3.2 \mathrm{mm} / \mathrm{s}$ . When the center of the loop is at
distance $r=1.5 b,$ what are (a) the magnitude of the magnetic flux
through the loop and (b) the current induced in the loop?

Key Concepts

Magnetic Field of a Current-Carrying Conductor

This concept involves calculating the magnetic field produced by a long, straight current-carrying wire. The strength of the magnetic field decreases with distance from the wire and is determined using Ampere’s or the Biot–Savart law, which provides the necessary framework for finding the magnetic field at any point in space around the wire.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is computed as the integral of the magnetic field over the surface area, taking into account both the magnitude and the orientation of the field relative to the area. This concept is fundamental in understanding how variations in magnetic fields interact with surfaces.

Faraday's Law of Electromagnetic Induction

Faraday’s law states that a change in magnetic flux through a closed circuit induces an electromotive force (emf) in the circuit. The induced emf is proportional to the rate at which the magnetic flux changes, making this principle central to the analysis of systems where motion or time-dependent magnetic fields result in electrical currents.

Ohm's Law in the Context of Induced Currents

Ohm’s law relates the voltage (or induced emf), current, and resistance in a circuit. When an emf is induced, Ohm’s law is used to determine the magnitude of the induced current by dividing the emf by the resistance. This connection is essential for predicting how the system responds to a changing magnetic environment.

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