example of vector potential
where is the position vector.
Proof. Using the entry nabla acting on products, we first may write
In the brackets the first product is, according to Euler’s theorem on homogeneous functions, equal to . The second product can be written as , which is , i.e. . The third product is, due to the sodenoidalness, equal to . The last product equals to (see the first formula (http://planetmath.org/PositionVector) for position vector). Thus we get the result
This means that has the vector potential (1).
|Title||example of vector potential|
|Date of creation||2013-03-22 15:42:56|
|Last modified on||2013-03-22 15:42:56|
|Last modified by||pahio (2872)|