Induced Electric Field Concept Question

[Dgray101]

I am having a bit of trouble understanding something in my textbook and was wondering if you guys could help clarify.

We just learned Faraday's Law that a time variant magnetic field will enduce an emf in a coil. What my textbook says is that " The electric field in the loop is NOT CONSERVATIVE because the line integral of E around a closed path is not zero. "

Can someone try to explain to me why an Electrostatic electric field is conservative yet this induced electric field is non-conservative?

 

[Simon Bridge]

What would happen if the induced field was conservative?

http://www.teachengineering.org/vie...lessons/van_mri_lesson_8/van_mri_lesson_8.xml

The electric fields produced by static charges are conservative, that is, a particle coming back to the same place will return to the same potential and kinetic energy. With a changing magnetic field the electric field is nonconservative, so charged particles may experience a gain in total energy. Where is this energy coming from? Well, whatever is responsible for changing the magnetic field must be producing currents to create the field in the first place, and so that agent must be the one adding energy to the system.​