A car drives onto a loop detector and increases the downward...

A car drives onto a loop detector and increases the downward component of the magnetic field within the loop from $1.2 \times 10^{-5} \mathrm{T}$ to $2.6 \times 10^{-5} \mathrm{T}$ in $0.38 \mathrm{s} .$ What is the induced emf in the detector if it is circular, has a radius of $0.67 \mathrm{m},$ and consists of four loops of wire? A. $0.66 \times 10^{-4} \mathrm{V}$ B. $1.5 \times 10^{-4} \mathrm{V}$ C. $2.1 \times 10^{-4} \mathrm{V}$ D. $6.2 \times 10^{-4} \mathrm{V}$

A car drives onto a loop detector and increases the downward component of the magnetic field within the loop from $1.2 \times 10^{-5} \mathrm{T}$ to $2.6 \times 10^{-5} \mathrm{T}$ in $0.38 \mathrm{s} .$ What is the induced emf in the detector if it is circular, has a radius of $0.67 \mathrm{m},$ and consists of four loops of wire?
A. $0.66 \times 10^{-4} \mathrm{V}$
B. $1.5 \times 10^{-4} \mathrm{V}$
C. $2.1 \times 10^{-4} \mathrm{V}$
D. $6.2 \times 10^{-4} \mathrm{V}$

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Key Concepts

Faraday's Law of Electromagnetic Induction

This principle states that a change in magnetic flux through a closed loop induces an electromotive force (emf) in the loop. It is central to understanding how varying magnetic fields can produce electrical currents in conductors.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field lines passing through a given area. It depends on both the strength of the magnetic field and the area over which the field is distributed, and its variation in time is what leads to induced emf according to Faraday's law.

Induced Electromotive Force (EMF)

Induced emf is the voltage generated in a circuit due to a changing magnetic flux. It is a manifestation of energy conversion, where a time-varying magnetic field transfers energy to electric charges, causing them to move.

Effect of Multiple Turns

When a coil consists of multiple loops or turns, the total induced emf is the sum of the emf induced in each individual loop. This means that the overall emf is multiplied by the number of turns, enhancing the effect of the magnetic flux change.

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