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

Young & Freedman Calc 14th Edition

Ch 29: Electromagnetic Induction

Problema 37e

Capitolo 29, Problema 37e

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. What is the magnitude of the induced emf if the radius in part (d) is 2R?

Guida verificata passo dopo passo

Understand that the problem involves electromagnetic induction, specifically Faraday's law of induction, which states that a changing magnetic field within a closed loop induces an electromotive force (emf) in the loop.

Recall Faraday's law of induction, which can be expressed as:

ε = - \frac{d Φ}{d t}

, where

ε

is the induced emf and

Φ

is the magnetic flux.

Calculate the magnetic flux

Φ

through a loop of radius 2R. The magnetic flux is given by:

Φ = B A

, where

B

is the magnetic field and

A

is the area of the loop. For a loop of radius 2R, the area is

A = π (2 R)^{2}

Substitute the expression for the area into the magnetic flux equation:

Φ = B π (2 R)^{2}

. Differentiate this expression with respect to time to find the rate of change of magnetic flux:

\frac{d Φ}{d t} = π (2 R)^{2} \frac{d B}{d t}

Apply Faraday's law to find the induced emf:

ε = - π (2 R)^{2} \frac{d B}{d t}

. The negative sign indicates the direction of the induced emf according to Lenz's law, which opposes the change in magnetic flux.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Faraday's Law of 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 proportional to the rate of change of the magnetic flux. In this scenario, the changing magnetic field within the solenoid induces an emf in the surrounding area.

Video consigliato:

Percorso guidato

09:26

Faraday's Law

Magnetic Flux

Magnetic flux is the product of the magnetic field and the area it penetrates, perpendicular to the field lines. It is a measure of the quantity of magnetism, considering the strength and extent of a magnetic field. Understanding how flux changes with the solenoid's radius is crucial for calculating the induced emf.

Video consigliato:

Percorso guidato

04:52

Magnetic Flux

Solenoid Magnetic Field

A solenoid is a coil of wire that generates a uniform magnetic field when an electric current passes through it. The magnetic field inside a long, straight solenoid is directly proportional to the current and the number of turns per unit length. The field's increase rate, dB/dt, is essential for determining the induced emf in the surrounding area.

Video consigliato:

Percorso guidato

13:54

Magnetic Field Produced by Loops and Solenoids

Pratica correlata

Domanda del libro di testo

A metal ring 4.50 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.250 T/s. What is the magnitude of the electric field induced in the ring?

2190

views

rank

Domanda del libro di testo

A long, thin solenoid has 400 turns per meter and radius 1.10 cm. The current in the solenoid is increasing at a uniform rate di/dt. The induced electric field at a point near the center of the solenoid and 3.50 cm from its axis is 8.00 × 10^-6 V/m. Calculate di/dt.

2564

views

rank

Domanda del libro di testo

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. What is the magnitude of the induced emf in a circular turn of radius R/2 that has its center on the solenoid axis?

1873

views

Domanda del libro di testo

A long, thin solenoid has 900 turns per meter and radius 2.50 cm. The current in the solenoid is increasing at a uniform rate of 36.0 A/s. What is the magnitude of the induced electric field at a point near the center of the solenoid and (a) 0.500 cm from the axis of the solenoid; (b) 1.00 cm from the axis of the solenoid?

2598

views

rank

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?

<Image>

1784

views

Domanda del libro di testo

The conducting rod ab shown in Fig. E29.29 makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. In what direction does the current flow in the rod?

1965

views