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

A car drives onto a loop detector and increases the downward-pointing 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. $0.66 \times 10^{-4} \mathrm{~V}$ C. $2.1 \times 10^{-4} \mathrm{~V}$ B. $1.5 \times 10^{-4} \mathrm{~V}$ D. $6.2 \times 10^{-4} \mathrm{~V}$

A car drives onto a loop detector and increases the downward-pointing 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. $0.66 \times 10^{-4} \mathrm{~V}$
C. $2.1 \times 10^{-4} \mathrm{~V}$
B. $1.5 \times 10^{-4} \mathrm{~V}$
D. $6.2 \times 10^{-4} \mathrm{~V}$

Key Concepts

Multiple Loops in a Coil

When a coil has multiple loops, the total induced emf is the sum of the emfs induced in each individual loop. This means that the net electromotive force is multiplied by the number of loops, making the overall effect more pronounced compared to a single loop.

Area of a Circular Loop

The area of a circular loop is a key geometric quantity needed to calculate the magnetic flux. It can be determined using the formula A = ?r², where r is the radius of the circle. This calculation helps in quantifying the region through which the magnetic field is penetrating, thus affecting the total flux.

Faraday's Law of Electromagnetic Induction

This principle states that any change in the magnetic flux through a circuit induces an electromotive force (emf) in that circuit. It quantifies the induced voltage as being proportional to the rate of change of the magnetic flux through the circuit, playing a fundamental role in understanding how electrical energy can be generated from changing magnetic fields.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is calculated as the product of the magnetic field strength, the area through which the field lines pass, and the cosine of the angle between the field direction and the normal to the area. Changes in magnetic flux are central to inducing an emf in a circuit.

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