30.7 : Induced Electric Fields: Applications

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.