How Does the Time Derivative of Electric Field Cross with Magnetic Field?

[gjfelix2006]

Hi, my question is the following:

<br /> \frac{\delta\vec E}{\delta t}\times \vec B = ?<br />
In other words, how can i develop this cross product.
Are there any identity that reduces this product?
Thanks.

 

[berkeman]

Do you have E as a function of time? What coordinate system are you taking the cross product in?

 

[gjfelix2006]

of course E is a function of time, and i think for simplicity the coordinate system is cartesian. Thanks

 

[StatusX]

There is the product rule d/dt(E x B) = dE/dt x B + E x dB/dt. That's about all I can tell you unless you give us what E and B are explicitly (which is what I think berkeman was asking).

 

[berkeman]

of course E is a function of time, and i think for simplicity the coordinate system is cartesian. Thanks

Fair enough. Take the derivative and use the determinant form of the cross product. That should get you what you need.

http://en.wikipedia.org/wiki/Cross_product