Ampere's Law has shown us how currents, moving electric charges, can create magnetic fields.

 

 

Faraday's Law has shown us how changing magnetic fields can induce an emf in a closed loop.

 

 

Now we are going to reinterpret Faraday's Law to see how the changing flux induces a nonconservative electric field in a coil.

 

 

Let's begin by placing a loop of wire outside of a solenoid whose counterclockwise current is going to be reduced gradually. In the first diagram, no current is induced in the outside loop because the current in the solenoid is steady. Once the current in the solenoid decreases, the magnetic field in the solenoid's core decreases and an emf will be induced in the wire loop.

 

      

 

The force that pushes the charges around the wire is F = qE, where E is the induced electric field. Since this force is parallel to the direction in which the charges are moving, it does work on them as they move around the loop.

 

 

Notice that this induced electric field is different from an electrostatic field created by a stationary point charge. When a test charge is moved along any given equipotential surface, no work is done by these conservative fields since the electric force acts perpendicular to the surface. Work can only be done when the force, or a component of the force, acts in the direction of motion. Or equivalently, work is done when the test charge is moved from one equipotential surface (voltage) to another.