Why Does Equation (7) in Magnetic Vector Potential Have a Negative Sign?

[fricke]

Not a homework question! I am doing exercises for upcoming final exam.

So, I get stuck at question 5.27 (Griffith 4th edition textbook).

Question:
Find the vector potential above and below an infinite uniform surface current with constant current sheet, K flowing at positive x direction.

I get really stuck so I googled the answer and it shows like this:
http://www.physicspages.com/2013/03/11/magnetic-vector-potential-of-an-infinite-wire/

What I don't understand is, from the link there, why does equation (7) need negative sign? I mean, we already obtain a nice solution in equation (5).

Help me please, thank you.

 

[PeterDonis]

Not a homework question! I am doing exercises for upcoming final exam.

That counts as homework as far as Physics Forums is concerned. This thread has been moved accordingly.

why does equation (7) need negative sign? I mean, we already obtain a nice solution in equation (5).

Equation (5) is not a solution for the vector potential, which is what you are supposed to find. It's a solution for the integral of the magnetic field over a given area, which is equal to the line integral of the vector potential around its boundary. Try comparing equation (5) with equation (6).