30.7: Induced Electric Fields: Applications

An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following equations represent the distinction between the two types of electric fields:

When the magnetic flux through a circuit changes, a nonconservative electric field is induced, which drives current through the circuit. However, when there is no conducting path in free space, it can be treated as if a conducting path were present; that is, nonconservative electric fields are induced wherever the magnetic flux through a circuit changes, whether or not a conducting path is present.

The induced electric field produced by a changing magnetic field differs from the electrostatic field generated by static charge distribution.

The induced electric field is non-conservative as its net work for moving a charge in a closed path is non-zero, whereas the electrostatic field is conservative.

Consider a circular coil with a 0.25 meter radius. A magnetic field perpendicular to the plane of the coil is directed inward and starts increasing at a constant rate of 3 t Tesla per second. Calculate the induced emf and electric field at 5 seconds.

List the known and unknown quantities.

As the magnetic field is perpendicular to the plane, the magnetic flux is a product of the coil's magnetic field and area.

Using Faraday's law, the induced emf based on the magnetic flux is 2.94 Volts at 5 seconds.

Also, induced emf can be expressed in terms of induced electric field.

As the electric field vector is tangential to the coil, whose circumference is 2-pi-r, the equation can be rearranged to find the induced electric field—1.87 Volts per meter.