Deriving the vector magnetic potential of magnetic dipole from a point of observation

[piash]

can anyone help me about deriving the vector magnetic potential of magnetic dipole from a point of observation????

i read D.K.CHENG & RAMO, but i couldn't understand, does anyone have any hand note of derivation of this ??? or any document that can help me to understand easily, precisely & step by step??

 

[piash]

Re: magnetic dipole

come on man, no one to help me????????//

 

[halls]

Re: magnetic dipole

can you be more specific? what is exactly what you don't understand?

 

[piash]

Re: magnetic dipole

i don't understand the way of deriving the equation of vector potential and magnetic flux. to derive that there have a term R which is defined as R² = r² + b² - 2rbcosψ,
where R is the point of observation in 3D spherical co-ordinates, b = radius in xy plane along angle Φ and ψ = angle between the linking point of origin and the point of observation P(r,θ,0) and b

 

[Jone]

Re: magnetic dipole

First we calculate the magnetic vector potential A. The formula for this contains a factor 1/R in the integrand. Then use the law of cosines R² = r² + b² - 2rb cos(ψ) for 1/R so that we get 1/R = 1/sqtr(r² + b² - 2rb cos(ψ)). Now do a binomial expansion for this. Then one can proceed either with the short and approximate derivation or the exact derivation. In the short version you keep only the first two terms. For the long and exact derivation one keeps all the terms in the binomial expansion and then notice that this can be written in terms of Legendre polynomials. Now you maybe know how to continue...