Induced Electric Fields: Exploring Gauss' & Lenz's Laws

In summary, when B changes in time, the Gauss' Law no longer applies and there are no sources of E. The lines of induced E are similar to B lines in magnetostatics, but have no start or end. Lenz's Law states that the electric field induced is exactly opposite to the change in magnetic field that causes it. This is represented by the relation between the curl of E and the time-dependent B, as well as the line integral of the tangential component.
  • #1
lighhhtworks
1
0
In electrostatics, × E = 0 so E that is a conservative field and there must be sources of E from which E flows. We know that this sources are the electrical charges given by Gauss' Law.

But when B changes in time, × E = - ∂ B / ∂t. Now the Gauss' Law no longer applies and if there are not net charges anywhere, there are no sources of E, so ∇ ⋅ E = 0.

So how are the lines of an induced E? Are they like B lines in magnetostatics? They just "turn" around something and they don't have any start or end?
And if they are, since Lenz's Law says that ε = - ∂φ / ∂t, are the lines of this E induced exactly the opposite of the B that induces it?

Please let me know if I'm not making my self clear, my english is not that good.
Thanks in advance!
 
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  • #2
Welcome to PF!

lighhhtworks said:
In electrostatics, × E = 0 so E that is a conservative field and there must be sources of E from which E flows. We know that this sources are the electrical charges given by Gauss' Law.

But when B changes in time, × E = - ∂ B / ∂t. Now the Gauss' Law no longer applies and if there are not net charges anywhere, there are no sources of E, so ∇ ⋅ E = 0.

So how are the lines of an induced E? Are they like B lines in magnetostatics? They just "turn" around something and they don't have any start or end?
And if they are, since Lenz's Law says that ε = - ∂φ / ∂t, are the lines of this E induced exactly the opposite of the B that induces it?

Yes, without charges, but with changing magnetic field, the electric field lines have neither start nor end. But Lenz's Law states that the electromotive force ε is exactly opposite to the change of B that induces it. The time-dependent B is related to the curl of the electric field: curl E = -∂B / ∂t, or in integral form: ## \oint Eds = -\partial φ / \partial t ## (the line integral of the tangential component along a closed curve is equal to the negative of the flux across the enclosed area).
 

Related to Induced Electric Fields: Exploring Gauss' & Lenz's Laws

What is an induced electric field?

An induced electric field is a type of electric field that is created when there is a change in magnetic flux through a conductor. This change in magnetic flux induces a current in the conductor, which creates an electric field.

What are Gauss' and Lenz's laws?

Gauss' law states that the flux of an electric field through a closed surface is equal to the charge enclosed by that surface. Lenz's law states that the direction of an induced current will be such that it opposes the change in magnetic flux that produced it.

How are Gauss' and Lenz's laws related to induced electric fields?

Gauss' and Lenz's laws are related to induced electric fields because they both explain the behavior of induced electric fields. Gauss' law helps us calculate the strength of the induced electric field, while Lenz's law helps us determine the direction of the induced current.

What are some real-world applications of induced electric fields?

Induced electric fields have many practical applications, such as in generators, transformers, and motors. They also play a crucial role in electromagnetic induction, which is used in wireless charging, induction cooktops, and magnetic levitation trains.

How can I explore Gauss' and Lenz's laws in an experiment?

There are many experiments that can be conducted to explore Gauss' and Lenz's laws. One simple experiment involves moving a magnet through a coil of wire and measuring the induced current. Another experiment could involve changing the distance between a magnet and a coil and observing the change in the induced current.

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