Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's have the equality (look to the the original question) $$ \int \limits_{-\infty}^{\infty} \left[ [\nabla_{\mathbf r'} \times \mathbf A (\mathbf r' )] \times \frac{\mathbf r' - \mathbf r}{|\mathbf r' - \mathbf r |^{3}}\right]d^{3}\mathbf r' = 4 \pi\mathbf A (\mathbf r). \qquad (.1) $$ I need to find the condition on the field, to which it must satisfy in order to satisfy the $(.1)$. By taking divergence $\nabla_{\mathbf r}$ of left and right sides of the equation, and changing the sequence of integration and divergence operations, I can get zero in the left side and $(\nabla \cdot \mathbf A)$ in the right side. But are integration and divergence operations commuting operations in case of $(.1)$?

This also solves my linked question.

share|cite|improve this question
Since $d^3\mathbf{r}'$ seems to be a volume element, what exactly is the domain of integration? Depending on wether the domain is 3-dimensional, the LHS should be scalar while the RHS is a vector field. – gofvonx Sep 16 '13 at 17:29
@gofvonx . The left side refer to vector field, as right. $d^{3}\mathbf r' = dx'dy'dz'$. – John Taylor Sep 16 '13 at 17:34

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.