Electric Field of an Electromagnet

As a beginning exercise in the use of Faraday's law, let us use Equation (i) to calculate the electric field of the electromagnet in Figure (1).

........(i)

We first argue that because of the circular symmetry, the electric field should travel in circles around the decreasing magnetic field. Thus we choose a circular path, shown in Figure (1), along which we will calculate . Then using the assumption (because of circular symmetry) that E is parallel to d and has a constant magnitude all the way around the circular path, we can write

........(1)

Using this result in Equation (i) gives

...........(2)

Figure 1:Using Faraday's law to calculate E.