# Question on conservative and non-conservative nature of electric fields.

1. Oct 4, 2015

### ovais

Hi all :)

I am about to finish the chapter of electromagnetic induction in my class. And I taught my students that the electric field induced due to changing magnetic flux is different that the electrostatic field due to stationary charges(Now I am wondering would it be wrong if I used the world electric field instead of electrostatic field, need this clarification also). One of my text says electric field can be conservative and non-conservative it does not especifically says electrostatic fields are conservative. So can I think electric field(not just electrostatic field) can be conservative and non-conservative?

Well as electromagnetic induction chapter is about to finish, I want to connect electricity and magnetic in the way they are. So I am studying this area and I found Maxwell's equations are doing this job.

The problem: I connect a wire loop to a battery. Their must be electric field set up within the wire, right? This electric field will apply force on each of the charge particle, Right? The free charge particles do move due to the force of the field, Right?
What is the direction of this force with respect to the instantaneous velocity of the charge?
Will their be any work done by the field on the charge during complete loop in the wire and inside the battery?

Finally what can I say about the conservative and non-conservative nature of the electric field that is set up in the wire loop?

Thanks a bunch.

Any help will be highly appreciated.

Last edited: Oct 4, 2015
2. Oct 4, 2015

### Chandra Prayaga

The electric field due to stationary charges is called electrostatic field. It is independent of time. This field is conservative. This means that if a charge is taken round on any closed path, the work done by the electric field is zero.
A time-dependent electric field (not called electrostatic) is non-conservative. This means that the work done by the field on a charge taken around a closed path is not zero.
Maxwell's equations completely determine all cases of electric and magnetic fields, including conservative fields.
If you connect a wire loop to a battery, the battery sets up an electric field in the wire. The electric field does work on the charge. Inside the battery, the battery provides the energy to push the (negative) charges at the positive terminal (low potential energy) to the negative terminal (high potential energy).
The instantaneous velocity of individual charges in the wire is randomly directed. The electric field superposes a drift velocity on top of the random velocity. This is discussed by the Drude model of conductivity, which is described in introductory textbooks on electricity & magnetism.

3. Oct 4, 2015

### ovais

Thanks for the reply Chandra. Your whole answer is good exactly upon the issue and I like it very much when you say,
But most of the things you said, are already in my head(my way of presenting my question is somewhat saggy). You however remind one thing very good when state about the instantaneous velocity of charge particles

But I feel my main question is still remains unanswered, that what can I say about the field that sets up in the wire loop when its connected to a batter? Conservative or Non-conservative?

You said work is done by the field it making the changes move so, should I say this field is non-conservative?
It doesn't appear time varying but is not electrostatic at the same time.

Thanks a bunch :)

Last edited: Oct 4, 2015