Getting E-Field from magnetic field intensity, H

[electrifice]

Homework Statement

Given the magnetic field intensity, H, find E.
H=[tex]\hat{y}[/tex]6cos(2z)sin((2x10^7)t - 0.1x)

Homework Equations

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

The Attempt at a Solution

Since we have H, we can use the relationship that [tex]\mu[/tex]H = B and then take the partial derivative of that with respect to time. That would give us this quantity...

[tex]\frac{- \partial B}{\partial t}[/tex]

Now, how do I get to E-field from that? How do you "uncurl" that?

 

[Mindscrape]

You could use Stokes's theorem to "uncurl" E. Do you see where it's headed?

Also, just to help you out in the future, anything with Calc 3 doesn't really belong in intro physics, and you may be helped quicker in advanced physics for questions like this.

 

[Moetasim]

To find the electric field, we can use Maxwell's equations, specifically the Faraday's law of induction which states that the curl of the electric field is equal to the negative of the time derivative of the magnetic field. In mathematical notation, this can be written as:

\nabla \times E = -\frac{\partial B}{\partial t}

Using this equation, we can solve for the electric field by taking the curl of both sides and rearranging to isolate for E. This would give us the following expression:

E = -\frac{1}{\mu}\nabla \times H

Where \mu is the magnetic permeability of the medium. This means that the electric field can be obtained by taking the curl of the given magnetic field intensity and dividing by the magnetic permeability. Keep in mind that the electric field will also have a time-dependent component, as shown in the given expression.