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corrected spelling of quadrupole and capitalised names
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edit approved Apr 11, 2014 at 2:56
suresh
edit approved Apr 11, 2014 at 2:56
suresh
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quadrapole quadrupole moment and higher for simple current loop

I'm working on a field configuration that needs to die off rapidly and I got to a $1/r^5$ dependence with canceling the dipole moment of the system cleverly, but to go get better arrangements I need to figure out the higher order moments of a simple loop as well.

Griffiths (page 243, 3rd ed) refers to this integral $\oint (r')^{n}P_n(cos \theta ') d L'$, with Pn$P_n$ as the legendreLegendre polynomials but I am unclear on how to go about evaluating it for higher moments because for the dipole term griffithsGriffiths does a clever trick that I'm not super sure extrapolates. I feel like the current loop is such a simple, tidy system it's higher moments would be tabulated somewhere just as an example of how higher orders are calculated, but I'm unable to find them after a few a days of googling and librarying.

quadrapole moment and higher for simple current loop

I'm working on a field configuration that needs to die off rapidly and I got to a $1/r^5$ dependence with canceling the dipole moment of the system cleverly, but to go get better arrangements I need to figure out the higher order moments of a simple loop as well.

Griffiths (page 243, 3rd ed) refers to this integral $\oint (r')^{n}P_n(cos \theta ') d L'$, with Pn as the legendre polynomials but I am unclear on how to go about evaluating it for higher moments because for the dipole term griffiths does a clever trick that I'm not super sure extrapolates. I feel like the current loop is such a simple, tidy system it's higher moments would be tabulated somewhere just as an example of how higher orders are calculated, but I'm unable to find them after a few a days of googling and librarying.

quadrupole moment and higher for simple current loop

I'm working on a field configuration that needs to die off rapidly and I got to a $1/r^5$ dependence with canceling the dipole moment of the system cleverly, but to go get better arrangements I need to figure out the higher order moments of a simple loop as well.

Griffiths (page 243, 3rd ed) refers to this integral $\oint (r')^{n}P_n(cos \theta ') d L'$, with $P_n$ as the Legendre polynomials but I am unclear on how to go about evaluating it for higher moments because for the dipole term Griffiths does a clever trick that I'm not super sure extrapolates. I feel like the current loop is such a simple, tidy system it's higher moments would be tabulated somewhere just as an example of how higher orders are calculated, but I'm unable to find them after a few a days of googling and librarying.

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Wolfram074
Wolfram074
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quadrapole moment and higher for simple current loop

I'm working on a field configuration that needs to die off rapidly and I got to a $1/r^5$ dependence with canceling the dipole moment of the system cleverly, but to go get better arrangements I need to figure out the higher order moments of a simple loop as well.

Griffiths (page 243, 3rd ed) refers to this integral $\oint (r')^{n}P_n(cos \theta ') d L'$, with Pn as the legendre polynomials but I am unclear on how to go about evaluating it for higher moments because for the dipole term griffiths does a clever trick that I'm not super sure extrapolates. I feel like the current loop is such a simple, tidy system it's higher moments would be tabulated somewhere just as an example of how higher orders are calculated, but I'm unable to find them after a few a days of googling and librarying.