Question

Two solenoids are part of the spark coil of an automobile. When the current in one solenoid falls from 6.0 A to zero in 2..5 $\mathrm{ms}$ , an emf of 30 $\mathrm{kV}$ is induced in the other solenoid. What is the mutual inductance $M$ of the solenoids?

Name: Problem 74, Chapter 30: Fundamentals of Physics
Uploaded: 2019-07-17T21:57:36-08:00
Duration: 1 min 14 s
Channel: Averell Hause
Description: Two solenoids are part of the spark coil of an automobile. When the current in one solenoid falls from 6.0 A to zero in 2..5 ms , an emf of 30 kV is induced in the other solenoid. What is the mutual inductance M of the solenoids?

   Two solenoids are part of the spark coil of an automobile.
When the current in one solenoid falls from 6.0 A to zero in 2..5 $\mathrm{ms}$ ,
an emf of 30 $\mathrm{kV}$ is induced in the other solenoid. What is the
mutual inductance $M$ of the solenoids?

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 30, Problem 74

Instant Answer

Solved by Expert Averell Hause

07/17/2019

Step 1

Step 1: We know that the induced emf ($\varepsilon$) is given by the formula: \[\varepsilon = -M \frac{dI}{dt}\] where $M$ is the mutual inductance, $I$ is the current, and $t$ is the time. Show more…

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Two solenoids are part of the spark coil of an automobile. When the current in one solenoid falls from 6.0 A to zero in 2..5 $\mathrm{ms}$ , an emf of 30 $\mathrm{kV}$ is induced in the other solenoid. What is the mutual inductance $M$ of the solenoids?

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Key Concepts

Faraday's Law of Electromagnetic Induction

This law states that a changing magnetic flux through a circuit induces an electromotive force (emf) in that circuit. In the context of mutual inductance, the law explains how a time-varying current in one coil creates a changing magnetic field, which in turn induces an emf in a nearby coil.

Mutual Inductance

Mutual inductance is a measure of the coupling between two circuits, quantifying how effectively a change in current in one circuit induces an emf in the other. It is defined by the relation between the induced emf and the rate of change of current in the adjacent circuit.

Rate of Change of Current

The rate of change of current (dI/dt) is a crucial factor in determining the induced emf in a circuit according to Faraday’s Law. It represents how quickly the current is changing over time, and in the formula for mutual inductance, a larger rate of change results in a higher induced voltage.

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