A motorcycle can increase the downward-pointing component of...

A motorcycle can increase the downward-pointing component of the magnetic field within a loop only from $1.2 \times 10^{-5}$ T to $1.9 \times 10^{-5}$ T. Suppose the detector is square, $0.75 \mathrm{~m}$ on a side, and has four loops of wire. Over what period of time must the magnetic field increase if it is to induce an emf of $1.4 \times 10^{-4} \mathrm{~V} ?$ A. $0.028 \mathrm{~s}$ C. $0.35 \mathrm{~s}$ B. $0.11 \mathrm{~s}$ D. $0.60 \mathrm{~s}$

A motorcycle can increase the downward-pointing component of the magnetic field within a loop only from $1.2 \times 10^{-5}$ T to $1.9 \times 10^{-5}$ T. Suppose the detector is square, $0.75 \mathrm{~m}$ on a side, and has four loops of wire. Over what period of time must the magnetic field increase if it is to induce an emf of $1.4 \times 10^{-4} \mathrm{~V} ?$
A. $0.028 \mathrm{~s}$
C. $0.35 \mathrm{~s}$
B. $0.11 \mathrm{~s}$
D. $0.60 \mathrm{~s}$

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Key Concepts

Rate of Change of Magnetic Field

The rate at which the magnetic field changes over time is key to determining the induced emf. When there is a small change in the magnetic field, the induced voltage can only be significant if this change occurs rapidly, as governed by the relationship in Faraday's Law.

Induced EMF in Multiple Loops

In devices with multiple loops or turns of wire, the induced emf is amplified by the number of loops. Each loop experiences a similar change in magnetic flux, so the total induced emf is the sum of the emfs generated in each loop, multiplying the basic effect of a single loop by the number of loops.

Magnetic Flux

Magnetic flux is a measure of the magnetic field passing through a given area. It is calculated as the product of the magnetic field strength and the area perpendicular to the field. When the field is uniform and the area is constant, the flux is given by ? = B × A.

Faraday's Law of Electromagnetic Induction

This fundamental law states that a changing magnetic flux through a circuit induces an electromotive force (emf) in that circuit. It relates the induced emf to the time rate of change of the magnetic flux, typically expressed as emf = -N (d?/dt), where N is the number of loops in the circuit and d?/dt is the rate of change of the magnetic flux.

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