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Ch 29: Electromagnetic Induction
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 29: Electromagnetic InductionProblema 1a
Capitolo 29, Problema 1a

A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. What emf is induced in this loop?

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1
Start by recalling Faraday's Law of Induction, which states that the induced electromotive force (emf) in a loop is equal to the negative rate of change of magnetic flux through the loop. The formula is: ε = -dΦdt, where Φ is the magnetic flux.
Calculate the initial magnetic flux through the loop using the formula: Φ = B A, where B is the magnetic field strength and A is the area of the loop. Substitute the given values: Φ = 3.80 T × 0.0900 m2.
Determine the rate of change of the magnetic flux. Since the magnetic field is decreasing at a constant rate, the change in magnetic flux can be expressed as: dΦdt = A dBdt. Substitute the area and the rate of change of the magnetic field: dΦdt = 0.0900 m2 × (-0.190 T/s).
Apply Faraday's Law to find the induced emf. Substitute the rate of change of magnetic flux into the formula: ε = -dΦdt. This will give you the magnitude of the induced emf.
Remember that the negative sign in Faraday's Law indicates the direction of the induced emf according to Lenz's Law, which states that the induced emf will generate a current that opposes the change in magnetic flux. However, for the magnitude, you can consider the absolute value.

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Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a loop induces an electromotive force (emf) in the loop. The induced emf is equal to the negative rate of change of magnetic flux through the loop. This principle is crucial for understanding how varying magnetic fields can generate electric currents.
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Faraday's Law

Magnetic Flux

Magnetic flux refers to the total magnetic field passing through a given area, such as a loop of wire. It is calculated as the product of the magnetic field strength, the area it penetrates, and the cosine of the angle between the field and the normal to the surface. In this problem, the magnetic field is perpendicular to the loop, simplifying the calculation of flux.
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Magnetic Flux

Rate of Change of Magnetic Field

The rate of change of the magnetic field is a key factor in determining the induced emf. In this scenario, the magnetic field is decreasing at a constant rate, which directly affects the rate of change of magnetic flux. Understanding this rate is essential for applying Faraday's Law to calculate the induced emf in the loop.
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05:30
Magnetic Fields and Magnetic Dipoles
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Domanda del libro di testo

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 6.0 × 10-5 T. What is the total magnetic flux through the coil before it is rotated? After it is rotated?

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Domanda del libro di testo

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 6.0 × 10-5 T. What is the average emf induced in the coil?

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Domanda del libro di testo

A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. If the loop has a resistance of 0.600 Ω, find the current induced in the loop.

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