- #1

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I'm stuck at an Electrodynamics problem and would be happy for some guidance

1. Homework Statement

1. Homework Statement

A magnetic dipole [itex]\vec{m}(t)=\vec{m}_0cos(\omega t)[/itex] at the origin can be described by the current density [itex]\vec{j}(\vec{r},t)=-\vec{m}(t)\times\vec{\nabla}\delta(\vec{r})[/itex]. Calculate the retarded potentials:

[itex]\Phi(\vec{r},t)[/itex] and [itex]\vec{A}(\vec{r},t)[/itex].

Given hint: "It is easier to first do the integration by parts and then transform the derivative with right to [itex]\vec{r}'[/itex] into the derivative with right to [itex]\vec{r}[/itex]".

## Homework Equations

[itex]\vec{A}(\vec{r},t)=\int_V\frac{\vec{j}(\vec{r},t)}{|\vec{r}-\vec{r}'|}d^3\vec{r}'[/itex]

[itex]\Phi(\vec{r},t)=\int_V\frac{\rho(\vec{r},t)}{|\vec{r}-\vec{r}'|}d^3\vec{r}'[/itex]

3. The Attempt at a Solution

3. The Attempt at a Solution

I tried calculating the x-component of the vector potential and got this:

[itex]A_x(\vec{r},t)=\int_V\frac{(m_y\partial_z-m_z\partial_y)}{|\vec{r}-\vec{r}'|}\delta(\vec{r}')d^3\vec{r}'

=\frac{(m_y\partial_z-m_z\partial_y)}{|\vec{r}-0|}[/itex]

Where eg. [itex]m_y[/itex] ist the y-component of the dipole vector. I get the last equation because of the delta distribution property [itex]\int^{\infty}_{\infty}f(x)\delta(x)dx=f(0)[/itex].

But this doesn't seem right, I didn't do any integration like the hint was suggesting.

Is this the right approach? I don't understand when I'm supposed to make use of the hint.

Kind regards

Alex