Suppose A is a vector satisfying curlA = aA, a a function of position.
Is it possible to turn the volume integral of A^2 into a surface integral? I know I have to write A^2 as the divergence of something, but what?
Suppose A is a vector satisfying curlA = aA, a a function of position.
Is it possible to turn the volume integral of A^2 into a surface integral? I know I have to write A^2 as the divergence of something, but what?
A couple of questions for clarification.
1. What quantities here are vector quantities, and which ones are scalar?
2. Which multiplication do you mean when you write Is that Or is it
3. I'm also curious as to what physical quantity represents. Is that the vector magnetic potential?
Ok, so re-writing your problem statement, I have the following:
Assume where is the vector magnetic potential defined by where is the magnetic field, and the scalar function depends only on the coordinates.
We wish to show that we can convert
into a surface integral via the divergence theorem.
The divergence theorem states that if is a continuously differentiable vector field defined on a neighborhood of then
Here's a question: do you know if is ever zero? Because, if not, you might be able to manipulate the equation
to simplify
I have another question: are you told that you can perform this transformation? Or are you merely trying to simplify a particular volume integral? If the second, can you provide a little more context?