Spatial dependence of induced Electric field

  • #1
The Faraday's law and Lenz's law together give you, $$\xi = -\frac{\partial\phi_B}{\phi t}$$ or put another way,$$\vec{\nabla} \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$$. My question, I am just asking to make sure, the spatial dependence of ##\vec \nabla \times \vec E## will be the same as the spatial dependence of ##\vec B##. So for example, if in a problem, the spatial extent of the magnetic field is restricted to a certain area then it is correct to assume that the closed lines of induced electric field will also be limited (circling the same) to the spatial extent of the magnetic field. Correct?
 
Last edited:

Answers and Replies

  • #2
Dale
Mentor
Insights Author
2021 Award
32,844
10,034
if in a problem, the spatial extent of the magnetic field is restricted to a certain area then it is correct to assume that the closed lines of induced electric field will also be limited (circling the same) to the spatial extent of the magnetic field. Correct?
No. In such a case ##\nabla \times E## will be spatially limited, but not necessarily E. The spatial extent of E is not the same as the spatial extent of ##\nabla \times E##
 
  • #3
Thanks a bunch!!!
 

Related Threads on Spatial dependence of induced Electric field

  • Last Post
2
Replies
42
Views
8K
  • Last Post
Replies
14
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
864
Replies
1
Views
938
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
7
Views
2K
Replies
2
Views
2K
Replies
7
Views
958
Top