Given the two vector fields:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\vec E and \vec B

[/tex]

Where the first is the electric vector field

and the second is the magnetic vector field, we

have the following identity:

[tex]

curl(\vec E) = -\frac{\partial \vec B } { \partial t }

[/tex]

and further that:

[tex]

curl(curl(\vec E)) = curl(-\frac{\partial \vec B } { \partial t })

= -\frac{\partial curl(\vec B) } {\partial t }

[/tex]

I tried to prove these by defining the vector fields:

[tex]

\vec E = C\frac{ \mathbf e_r } {p^2}

[/tex]

and

[tex]

\vec B = <0, 0, B>

[/tex]

where C and B are constants. But I ended up with

zero for curl(E), which cannot be right. So my reasoning

is in error somewhere.

Any insight appreciated.

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# The curl of certain vector fields

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