Skip to main content
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 39
Capitolo 29, Problema 39

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.

Guida verificata passo dopo passo
1
Start by understanding the concept of electromagnetic induction in solenoids. When the current in a solenoid changes, it induces an electric field around it. This is described by Faraday's law of induction.
Use the formula for the induced electric field inside a solenoid: E = rRdidt, where E is the induced electric field, r is the distance from the axis, R is the radius of the solenoid, and didt is the rate of change of current.
Substitute the given values into the formula: 8.00×10-6 for E, 3.50 cm for r, and 1.10 cm for R. Convert these distances to meters.
Rearrange the formula to solve for didt: didt = ERr.
Calculate the value of didt using the rearranged formula and the substituted values.

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:
9m

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 changing magnetic field within a closed loop induces an electromotive force (EMF) in the loop. In the context of a solenoid, the changing current alters the magnetic field inside, inducing an electric field around the solenoid. This principle is crucial for understanding how the rate of change of current (di/dt) affects the induced electric field.
Video consigliato:
Percorso guidato
09:26
Faraday's Law

Magnetic Field Inside a Solenoid

The magnetic field inside a long, thin solenoid is uniform and given by B = μ₀nI, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. This concept helps in understanding how the solenoid's properties and current contribute to the magnetic field, which is essential for calculating the induced electric field.
Video consigliato:
Percorso guidato
05:22
Magnetic Field Inside a Solenoid

Induced Electric Field

The induced electric field around a solenoid is related to the rate of change of the magnetic field inside it. According to Faraday's Law, the magnitude of the induced electric field at a distance from the solenoid's axis can be calculated using the formula E = (r/2) * (dB/dt), where r is the radial distance from the axis. This concept is key to determining the relationship between di/dt and the given electric field.
Video consigliato:
Percorso guidato
03:16
Intro to Electric Fields
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?

<Image>

1967
views
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 if the radius in part (d) is 2R?

2041
views
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?

<Image>

1427
views
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
1
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