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Ch 30: Electromagnetic Induction
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 30: Electromagnetic InductionProblema 38
Capitolo 30, Problema 38

A 100-turn, 2.0-cm-diameter coil is at rest with its axis vertical. A uniform magnetic field 60° away from vertical increases from 0.50 T to 1.50 T in 0.60 s. What is the induced emf in the coil?

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Determine the formula for the induced emf using Faraday's Law of Induction: \( \text{emf} = -N \frac{\Delta \Phi_B}{\Delta t} \), where \( N \) is the number of turns, \( \Delta \Phi_B \) is the change in magnetic flux, and \( \Delta t \) is the time interval.
Calculate the magnetic flux \( \Phi_B \) using the formula \( \Phi_B = B A \cos \theta \), where \( B \) is the magnetic field strength, \( A \) is the area of the coil, and \( \theta \) is the angle between the magnetic field and the normal to the coil's surface.
Find the area of the coil using the formula for the area of a circle: \( A = \pi r^2 \), where \( r \) is the radius of the coil. The radius is half the diameter, so \( r = 0.02 \, \text{m} / 2 \).
Calculate the change in magnetic flux \( \Delta \Phi_B \) by substituting the initial and final values of \( B \) into the flux formula: \( \Delta \Phi_B = (B_\text{final} A \cos \theta) - (B_\text{initial} A \cos \theta) \).
Substitute the values for \( N \), \( \Delta \Phi_B \), and \( \Delta t \) into the formula for induced emf to find the result: \( \text{emf} = -N \frac{\Delta \Phi_B}{\Delta t} \). Note that the negative sign indicates the direction of the induced emf according to Lenz's Law.

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Faraday's Law of Electromagnetic Induction

Faraday's Law states that the induced electromotive force (emf) in a closed loop is directly proportional to the rate of change of magnetic flux through the loop. This principle is fundamental in understanding how a changing magnetic field can generate an electric current in a conductor.
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Faraday's Law

Magnetic Flux

Magnetic flux is defined as the product of the magnetic field strength and the area through which the field lines pass, adjusted for the angle between the field and the normal to the surface. It quantifies the total magnetic field passing through a given area and is crucial for calculating the induced emf.
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04:52
Magnetic Flux

Lenz's Law

Lenz's Law states that the direction of the induced current will be such that it opposes the change in magnetic flux that produced it. This law helps determine the polarity of the induced emf and ensures the conservation of energy in electromagnetic systems.
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11:07
Lenz's Law
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