I have this question to write down the vector potentials for four straight wires parallel to the $z$-axis cross the $xy$-plane at the vertices of a square: $(a, a), (a, −a), (−a, a)$ and $(−a, −a)$. The wires through points $(a, a)$ and $(−a, −a)$ carry current $I$ in the positive $z$-direction; the wires through $(a, −a)$ and $(−a, a)$ carry current $I$ in the negative $z$-direction.
I have already worked out the formula for the vector potential ($A(x,y)$) which is:
$A(x,y)=-\frac{\mu_0k}{4\pi}I\ln(x^2+y^2)$
But I'm struggling to see how to write down the vector potential for this case.
Is this the answer?
$A(x,y)=-\frac{\mu_0k}{4\pi}I\ln((x-a)^2+(y-a)^2+(x-a)^2+(y+a)^2+(x+a)^2+(y-a)^2+(x+a)^2+(y+a)^2)$