What is Meant by 'Outer' Differentiation in Vector Potential?

[Creator]

"outer" differentiation?

Since I didn't get a response on the "Diff. Eqns." thread, I put it here.

Can someone give me a clear explanation of what is meant by "outer" differentiation.

As for example, when we differentiate the vector potential, dA/dx, in order to arrive at the magnetic field, B, why would this be called an 'outer' differentiation??


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[turin]

Originally posted by Creator
... when we differentiate the vector potential, dA/dx, in order to arrive at the magnetic field, B, why would this be called an 'outer' differentiation??

Probably because d/dx is not exactly what you do. You take the cross product of the gradient operator with the vector potential to get the magnetic field. The cross product is sometimes called/related to the outer product, but that's tensor jargon with which I am unfamiliar.

 

[Creator]

Thanks for the response, Turin;

and thanks for the correction. Oc course, you are accurate in saying it is the cross product of the gradient.
I guess then if someone says "dA/dt is the outer differentiation" I should interpret that to mean they are simply referring to it as being a cross product.??

 

[turin]

Originally posted by Creator
... if someone says "dA/dt is the outer differentiation" I should interpret that to mean they are simply referring to it as being a cross product.??

I would ask them what they mean. I wouldn't know how to make sense of that.