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Chapter 27: Problem 5

Can an induced electric field exist in the absence of a conductor?

Short Answer

Expert verified
Yes, an induced electric field can exist in the absence of a conductor, as long as there is a changing magnetic field present. Faraday's law of electromagnetic induction, which doesn't necessitate the presence of a conductor, supports this statement.

Step by step solution

01

Understanding Basic Concepts

Firstly, an induced electric field is one that is produced as a result of a changing magnetic field. This phenomenon is known as electromagnetic induction. The general association of electric fields is that they are produced by electric charges, and these could be from a conductor. However, in the context of electromagnetic induction, the charges which cause the changes in the magnetic field leading to the induction of the electric field, could be elsewhere and are not restricted to being in a conductor.
02

Applying Faraday's Laws of Electromagnetic Induction

According to Faraday's law, a changing magnetic field will induce an EMF (Electromotive Force) and hence an electric field. This law does not specify the need for a conductor. Thus, theoretically, even in the absence of a conductor, a varying magnetic field can induce an electric field. The magnetic field need not be changing within a conductor; it can be changing in open space.
03

Conclusion

In conclusion, although it's often easier to study and utilize induced electric fields in the context of conductors (since they allow for the flow of electric charges, thereby forming electric currents which we can easily measure), it's perfectly plausible for an induced electric field to exist in the absence of a conductor as long as there is a changing magnetic field present. Thus, an induced electric field can indeed exist in the absence of a conductor.

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Most popular questions from this chapter

Show that the volt is the SI unit for the rate of change of magnetic flux, making Faraday's law dimensionally correct. Your result also shows why the unit of flux itself can be expressed as \(\mathrm{V} \cdot \mathrm{s}.\)

A long, straight coaxial cable consists of two thin, tubular conductors, the inner of radius \(a\) and the outer of radius \(b\). Current \(I\) flows out along one conductor and back along the other. Show that the self-inductance per unit length of the cable is \(\frac{\mu_{0}}{2 \pi} \ln (b / a)\)

A conducting disk with radius \(a\), thickness \(h,\) and resistivity \(\rho\) is inside a solenoid of circular cross section, its axis coinciding with the solenoid axis. The magnetic field in the solenoid is given by \(B=b t,\) where \(b\) is a constant. Find expressions for (a) the current density in the disk as a function of the distance \(r\) from the disk center and (b) the power dissipation in the entire disk. (Hint: Consider the disk as consisting of infinitesimal conducting loops.)

A flip coil is used to measure magnetic fields. It's a small coil placed with its plane perpendicular to a magnetic field, and then flipped through \(180^{\circ} .\) The coil is connected to an instrument that measures the total charge \(Q\) that flows during this process. If the coil has \(N\) turns, area \(A\), and resistance \(R,\) show that the field strength is \(B=Q R / 2 N A.\)

A 1250 -turn solenoid \(23.2 \mathrm{cm}\) long and \(1.58 \mathrm{cm}\) in diameter carries 165 mA. How much magnetic energy does it contain?
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