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## Homework Statement

Determine the vector potential due to a short wire running from (−L/2, 0, 0) to (L/2, 0, 0) carrying a current I = I

_{0}cos(ωt) (consider only points at distance r >> L from the origin). (You may neglect the effect of the return circuit.) Now determine the corresponding scalar potential for large r.

## Homework Equations

V(

__x,__t) = 1/4πε

_{0}∫d

^{3}

__x'__ρ(

__x'__, t - |

__x'__-

__x|__/c) / |

__x'__-

__x|__

A(

A

__x,__t) = μ

_{0}/4π ∫d

^{3}

__x'__

__j__(

__x'__, t - |

__x'__-

__x|__/c) / |

__x'__-

__x|__

Where A is the vector potential and V is the scalar potential.

## The Attempt at a Solution

I managed to solve the first part for the vector potential by using the fact that r>>L and therefore |

__x'__-

__x|__≈ r

and using that

__j__= I/c

**x**(hat) (in the x direction, and I let C= the cross sectional area of the wire)

this gave

__A__(

__x,__t) = (μ

_{0}L I

_{0}cos(ω(t-r/c)))/4πr

When trying to determine the vector potential I ran into an issue, I'm not entirely sure what ρ is explicitly. I had a guess that is was ρ = Q/LC, and then using the fact that I=dQ/dt and integrating to find Q, but this was a stab in the dark and I have no idea if it's right.

Any help would be greatly appreciated, thank you!