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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 40e
Capitolo 29, Problema 40e

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. If the ring is cut at some point and the ends are separated slightly, what will be the emf between the ends?
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Guida verificata passo dopo passo
1
Understand that the problem involves electromagnetic induction, specifically Faraday's law of induction, which states that a changing magnetic field within a loop induces an electromotive force (emf) in the loop.
Identify that the magnetic field is decreasing at a rate of -0.0350 T/s. This rate of change of the magnetic field is crucial for calculating the induced emf.
Use Faraday's law of induction, which is given by the formula: ε=-dΦ/dt, where ε is the induced emf and Φ is the magnetic flux.
Calculate the magnetic flux Φ using the formula: Φ=BA, where B is the magnetic field and A is the area of the circle. Since the magnetic field is uniform, the flux is simply the product of the field and the area.
Substitute the rate of change of the magnetic field into Faraday's law to find the induced emf: ε=-A(-0.0350). The negative sign in Faraday's law indicates the direction of the induced emf, but since the field is decreasing, the induced emf will be positive.

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Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in the circuit. The induced emf is proportional to the rate of change of the magnetic flux. In this scenario, the decreasing magnetic field within the circle causes a change in magnetic flux, which induces an emf in the ring.
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Percorso guidato
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Faraday's Law

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, considering the strength and extent of a magnetic field. It is calculated as the product of the magnetic field (B) and the area (A) it penetrates, perpendicular to the field. In this problem, the change in magnetic flux due to the decreasing magnetic field is crucial for determining the induced emf.
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Percorso guidato
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Magnetic Flux

Lenz's Law

Lenz's Law states that the direction of the induced emf and current will be such that it opposes the change in magnetic flux that produced it. This principle helps determine the polarity of the induced emf in the ring when the magnetic field decreases. It ensures that the induced current creates a magnetic field opposing the reduction in the original field.
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11:07
Lenz's Law
Pratica correlata
Domanda del libro di testo

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. What is the emf between points a and b on the ring?

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Domanda del libro di testo

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. What is the current in the ring if its resistance is 4.00 Ω?

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Domanda del libro di testo

A parallel-plate, air-filled capacitor is being charged as in Fig. 29.23. The circular plates have radius 4.00 cm, and at a particular instant the conduction current in the wires is 0.520 A. What is the rate at which the electric field between the plates is changing?

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Domanda del libro di testo

A long, straight solenoid with a cross-sectional area of 8.00 cm2 is wound with 90 turns of wire per centimeter, and the windings carry a current of 0.350 A. A second winding of 12 turns encircles the solenoid at its center. The current in the solenoid is turned off such that the magnetic field of the solenoid becomes zero in 0.0400 s. What is the average induced emf in the second winding?

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Domanda del libro di testo

A parallel-plate, air-filled capacitor is being charged as in Fig. 29.23. The circular plates have radius 4.00 cm, and at a particular instant the conduction current in the wires is 0.520 A. (a) What is the displacement current density jD in the air space between the plates?

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Domanda del libro di testo

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. What is the shape of the field lines of the induced electric field shown in Fig. E29.15 , within the colored circle?

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