Help! Understanding Faraday's Law

[arnesmeets]

I've got some serious problems understanding Faradays law.

I think any changing magnetic field will create/induce an electric field through empty space. Is that correct? And if so, what is the direction of the field? I mean, the electric field vectors must have *some* direction, but I can't possibly imagine which direction that should be. Everything I try gives me some sort of contradiction. I also read that this electric field is "not conservative". I don't really understand what is meant by this and how it can be "not conservative", can someone please clarify?

And how can you find the magnitude of the electric field? For example, in the concrete situation where B varies as $$B = B_0 \sin \omega t$$ - how do I calculate E?? I can calculate the time derivative of the flux through some imaginary closed loop, but whenever I try to calculate E, I get some weird result.

Could someone please explain? I really don't understand this stuff.

 

[vsage]

What is your "weird result"? Also, a conservative force is one that exerts the same amount of work in moving an object from point A to point B regardless of path.

 

[arunbg]

According to Faraday-Lenz's law ,
$$\epsilon = - \frac{d\phi}{dt}$$

where $\phi$ is the magnetic flux through a given area .
The tendency of the induced electric field or induced emf is to oppose any change in magnetic flux through a given area, as can be seen from the -ve sign on the RHS of the equation .The induced electric field itself produces a magnetic field which tends to nullify the change.
Now can you figure out the direction of electric field in different cases ?

For the second part of your question, you need a path along which the electric field is uniform.
Let us consider the varying field being directed out of the plane of the computer screen . From arguments of symmetry, we may conclude that the electric fields induced are circular and lie parallel to the plane of the screen (find the direction of magnetic field induced at some instant) .For a fixed path of radius r, you can find flux through the circular area and calculate emf .
You know that
$$\int E.dl = \epsilon$$

Can you go from here ?

Arun

 

[arnesmeets]

So the induced electric field shouldn't be seen as the "classical" electric field (having a magnitude and direction etc) but rather as a sort of "friction force"? The direction of the induced electric field depends on how the flux is changing? What happens in empty space then, if the magnetic flux is changing - there must be SOME electric field, but we just cannot say how it looks, what its direction is?

Also, I don't really get why the fields induced should be circular in that particular situation...

 

[arunbg]

So the induced electric field shouldn't be seen as the "classical" electric field (having a magnitude and direction etc) but rather as a sort of "friction force"?

Well, not really. It does indeed have a magnitude and direction, but the electric field tends to form closed paths.
The problem with this is that even though work is done on a unit charge by the electric field , it always seems to return to its original configuration (closed path) or same potential and seemingly no work is done .
It is therefore emphasised that the notion of potential is absent ( or shall we say different) in the case of induced fields.
And this is also why it is non conservative .

The direction of the induced electric field depends on how the flux is changing?

Yes , that is correct .

Also, I don't really get why the fields induced should be circular in that particular situation...

Have you learned about the magnetic fields produced by a circular current carring conductor or solenoid ?
How are they directed ? What is the direction of electric field in the conductor ? Is it same as that of conventional current ?
How can you use these fields to oppose flux change ?

 

[arnesmeets]

I sort of get that, I think (about the field forming closed paths etc).

But there is one problem left for me: let's look at the path the charge is following. Is the induced field tangent to the path, or is it perpendicular to the tangent, or... ? I really don't see this.

 

[arunbg]

All other aspects of an induced electric field is the same as that of an ordinary electric field .
So the direction of the induced electric field is the direction in which a charged particle will move when placed in the field .

Also try to answer the questions in the second part of my last post .

Arun