Question

A flat, rectangular coil of dimensions $l$ and $w$ is pulled with uniform speed $v$ through a uniform magnetic field $B$ with the plane of its area perpendicular to the field (Fig. $\mathbf{E} 2 \mathbf{9} . \mathbf{1 2}$ ). (a) Find the emf induced in this coil. (b) If the speed and magnetic field are both tripled, what is the induced emf?

Name: Problem 12, Chapter 25: University Physics with Modern Physics
Uploaded: 2021-02-23T17:38:02-08:00
Duration: 3 min 43 s
Channel: Vishal Gupta
Description: A flat, rectangular coil of dimensions l and w is pulled with uniform speed v through a uniform magnetic field B with the plane of its area perpendicular to the field (Fig. 𝐄 2 9 . 1 2 ). (a) Find the emf induced in this coil. (b) If the speed and magnetic field are both tripled, what is the induced emf?

   A flat, rectangular coil of dimensions $l$ and $w$ is pulled with uniform speed $v$ through a uniform magnetic field $B$ with the plane of its area perpendicular to the field (Fig. $\mathbf{E} 2 \mathbf{9} . \mathbf{1 2}$ ). (a) Find the emf induced in this coil. (b) If the speed and magnetic field are both tripled, what is the induced emf?

University Physics with Modern Physics

Roger A. Freedman,… 15th Edition

Chapter 25, Problem 12

Instant Answer

Solved by Expert Vishal Gupta

02/23/2021

Step 1

In this case, the magnetic field is perpendicular to the coil, so $\theta = 0$ and $\cos\theta = 1$. Therefore, the magnetic flux is given by: \[\Phi = B \cdot A \cdot \cos\theta = B \cdot A\] Show more…

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A flat, rectangular coil of dimensions $l$ and $w$ is pulled with uniform speed $v$ through a uniform magnetic field $B$ with the plane of its area perpendicular to the field (Fig. $\mathbf{E} 2 \mathbf{9} . \mathbf{1 2}$ ). (a) Find the emf induced in this coil. (b) If the speed and magnetic field are both tripled, what is the induced emf?

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Key Concepts

Faraday's Law of Electromagnetic Induction

This law establishes that a change in magnetic flux through a closed loop induces an electromotive force (emf) in that loop. It is expressed as the rate of change of flux, making it fundamental in analyzing how moving conductors or varying fields generate voltage in circuits.

Magnetic Flux

Magnetic flux quantifies the amount of magnetic field passing through a specified area and is calculated as the product of the magnetic field strength and the perpendicular component of the area. It is critical for understanding how changes in either the field or the area lead to an induced emf.

Motional EMF

Motional emf arises when a conductor moves through a magnetic field, resulting in a change in magnetic flux linked with the conductor. This concept explains how mechanical motion, such as the movement of a coil, leads to the generation of an electrical signal and is central in the operation of many electromagnetic devices.

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