{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MagneticMoment - Magnetic Moment Ian R Gatland Georgia...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Magnetic Moment. Ian R. Gatland, Georgia Institute of Technology Physics 3122 Notes, July 22, 2010 Preliminaries. Consider a vector field, J ( r ) , that is localized (zero on and outside a surface S surrounding a volume Γ ) and divergence free ( J = 0 ) together with two scalar fields, f ( r ) and g ( r ) . Then [ f J g + Γ g J f ] d τ = [ f J g + ( fg J ) Γ f ( g J )] d τ = ( fg J ) Γ d τ + [ f J g Γ fg J f J g ] d τ = fg J S d a fg J d τ = 0 Γ (1) using the localization and divergence conditions. Case 1: Equation (1) with f = 1 and g = x provides [ J x + Γ x J 1] d τ = [ J ˆ x + Γ 0] d τ = J x Γ d τ = 0 (2) and similar results with y and z in place of x . Case 2: Equation (1) with f = x and g = x provides [ x J x + Γ x J x ] d τ = 2 xJ x Γ d τ = 0 (3)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}