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Faraday's law and a uniform magnetic field

  • Thread starter ehrenfest
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[SOLVED] faraday's law

1. Homework Statement
A uniform magnetic field [itex]\mathbf{B}(t)[/itex] in the z-direction, fills a circular region in the x-y plane. If B is changing with time, what is the direction of [itex]\mathbf{E}[/itex]/


2. Homework Equations



3. The Attempt at a Solution
My book says it is circumferential, just like the magnetic field inside a long straight wire carrying a uniform current density.

Apparently they are using the analogy between Faraday's Law and Ampere's Law. But I do not see the logic at all.

This is Griffiths Example 7.7.
 

Answers and Replies

Ben Niehoff
Science Advisor
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They are mathematically very similar. Faraday's law:

[tex]\nabla \times \vec E = -\frac{\partial \vec B}{\partial t}[/tex]

And Ampere's Law (for electrostatics):

[tex]\nabla \times \vec B = \mu_0 \vec J[/tex]
 
1,996
1
I know, but why does that imply that the E-field is circumferential?
 
Ben Niehoff
Science Advisor
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Because [itex]\partial \vec B / \partial t[/itex] is vertical.
 

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