# Different results for Magnetic field using different methods In calculating the magnetic field created by this current at the center point of the loop using Biot-Savart and using the vector potential will there be a difference? If so what is it and why?

Using Biot-Savart the Magnetic field is simply a superposition of fields created by straight wire and loop. But how does one calculate the vector potential at the center?

• Have you tried it and gotten a difference? If so, it would help if you summarize or show your calculations. Dec 7 '11 at 19:02

The vector potential at point $x$ can be calculated as the integral over the wire of the vector current divided by the distance to $x$. Take the curl of the resulting expression, move the curl inside the integral sign, do a few manipulations and wala!, you've got the Biot-Savart law! They are exactly the same.
• I see what's bothering you, the 1/r divergence. That disappears when you differentiate under the integral sign. $\partial_{x} \int dy A(x,y) = \int dy \partial_{x} A(x,y)$. A mathematician might take offense. Dec 9 '11 at 7:58