30.6: Induced Electric Fields

The fact that emfs are induced in circuits implies that work is being done on the conduction electrons in the wires. What can possibly be the source of this work? We know that it’s neither a battery nor a magnetic field, as a battery does not have to be present in a circuit where current is induced, and magnetic fields never do any work on moving charges. The source of the work is in fact an electric field that is induced in the wires. For example, if a stationary conductor is placed in a changing magnetic field, an induced current starts flowing in the conductor. The source of this induced current is an electric field that is produced due to a change in magnetic flux. This field is called the induced electric field.

The work done by an induced electric field in moving a unit charge completely around a circuit is the induced emf, ε; that is,

where ∮ represents the line integral around the circuit. Faraday’s law can be written in terms of the induced electric field as

Thus, both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday’s law.

If a stationary conductor is placed in a changing magnetic field, an induced current starts flowing in the conductor.

The source of this induced current is an electric field that is produced due to a change in magnetic flux. This field is called the induced electric field.

Consider a solenoid having 'n' number of turns per unit length. Current 'I' is passed in the solenoid, which produces a magnetic field 'B'.

A conducting loop attached to a galvanometer is placed around the solenoid.

If the current in solenoid winding increases, the magnetic flux will also increase, and an induced current is produced in the conducting loop due to the induced electric field 'E'.

According to Faraday’s law, an electromotive force is also produced in the conducting loop.

Also, the work done by the induced electric field is the line integral around a closed path and is equal to the induced electromotive force.

Thus, Faraday's law can be restated in terms of the induced electric field.