Electric Field of Static Charges

If all we have around are static electric charges, then there are no magnetic fields, no magnetic flux, and no changing magnetic flux. For this special case, dΦ_B/dt = 0 and Faraday’s law gives
......(1)
When the line integral of a force is zero around any closed path, we say that the force is conservative. Thus we see that if we have only static electric charge (or constant magnetic fields), the electric field is a conservative field. In contrast, if we have changing magnetic fields, if dΦ_B/dt is not zero, the electric field is not conservative.
This can lead to some rather interesting results which we will see in our discussion of a device called the betatron.