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 $2.6 \times 10^{-5} \mathrm{Tin} 0.38 \mathrm{s} .$ 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. $0.66 \times 10^{-4} \mathrm{V} \quad$ B. $1.5 \times 10^{-4} \mathrm{V}$ C. $2.1 \times 10^{-4} \mathrm{V} \quad$ 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 $2.6 \times 10^{-5} \mathrm{Tin} 0.38 \mathrm{s} .$ 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. $0.66 \times 10^{-4} \mathrm{V} \quad$ B. $1.5 \times 10^{-4} \mathrm{V}$
C. $2.1 \times 10^{-4} \mathrm{V} \quad$ D. $6.2 \times 10^{-4} \mathrm{V}$

Key Concepts

Faraday's Law of Electromagnetic Induction

This principle states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in the loop. The induced emf is proportional to the negative rate of change of the magnetic flux, which is mathematically expressed as emf = -d?/dt. This concept forms the basis for understanding how mechanical motion or varying magnetic fields can generate electrical voltage in a coil.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field passing through a given area, defined as the product of the magnetic field strength and the area perpendicular to the direction of the field. It is an essential concept in electromagnetic induction, as changes in magnetic flux over time are what induce emf according to Faraday's Law.

Loop Geometry and Area Calculation

The area of the loop is crucial when calculating magnetic flux, especially when dealing with circular loops. The area of a circle is given by ?r², where r is the radius. This geometric factor determines how much of the magnetic field interacts with the loop, which in turn affects the induced emf.

Multiplying Number of Loops (Coils)

When a coil consists of multiple loops, the total induced emf is the sum of the emf induced in each individual loop. This is accounted for by multiplying the emf calculated for one loop by the number of loops (turns). This concept is important in practical applications where multiple loops are used to enhance the induced emf.

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