• Support PF! Buy your school textbooks, materials and every day products Here!

E-induced lines

  • #1
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!
 

Answers and Replies

  • #2
ehild
Homework Helper
15,427
1,827
Welcome to PF!

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 Threads on E-induced lines

Replies
4
Views
11K
  • Last Post
Replies
4
Views
567
Replies
6
Views
9K
  • Last Post
Replies
14
Views
3K
Replies
1
Views
12K
Replies
6
Views
4K
  • Last Post
Replies
3
Views
490
Replies
6
Views
414
Replies
2
Views
17K
Top