How Does Magnetostatics Explain Zero Divergence and Vector Potentials?

[_Syzygy_]

Hi :)

this is my first post to this forum. I am doing some study in EM
and I've come across some helpful hints on here, to help me through some problems. However i have come across a couple stumbling blocks.
if anyone could give me a couple clues to go about working these out and give me a direction to go in, it would be much appreciated. cheers in Advance.

1) how that for static fields (no time dependece and only currents of finite extent) the divergence potential is zero, i.e., \nabla\cdotA = 0
(note the A is a vector)

2) We found that for static fields the vector potential obeys
\nabla^2 A = - \mu oj . Show that from this equation follows that \nabla\times B = \mu oj

again A, B, and j are vectors.

hope my latex works..

thanks again

 

[HallsofIvy]

What is the relationship between A and B?

 

[_Syzygy_]

Hi HallsofIvy

Thanks for your reply.

these two are from a four set of question i had been looking at.
The first asked "to compute the magnetic flux density B for a point P due to the electric current I in a long, straight wire (distance between wire and point p is \rho
Using biot-savart law i came up with the following

\frac{\mu_o I}{2 \pi\rho} a

this may not look exactly as what i got as I am still unsure about using Latex.

The second part, asked, to compute the vector potential and magnetic flux density for a point P located between two parallel (straight) wires (distance between the wires is D) carrying electric currents of the same magnitude I in opposite directions.
I completed this and proceeded onto looking at the two i had asked on here, but wasnt sure what to do with those 2. I've been back over the second part however and I am re-working it, think I've made mistake in it's working out.

i assume you were asking the relationship from therre first two parts that i determined?