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## Electromagnetism

by: Miss Lucienne Hamill

14

0

2

# Electromagnetism PHY 712

Miss Lucienne Hamill
WFU
GPA 3.91

Natalie Holzwarth

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COURSE
PROF.
Natalie Holzwarth
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Physics 2

This 2 page Class Notes was uploaded by Miss Lucienne Hamill on Wednesday October 28, 2015. The Class Notes belongs to PHY 712 at Wake Forest University taught by Natalie Holzwarth in Fall. Since its upload, it has received 14 views. For similar materials see /class/230730/phy-712-wake-forest-university in Physics 2 at Wake Forest University.

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Date Created: 10/28/15
February 28 2000 Notes for Lecture 19 Magnetic dipole eld These notes are very similar to the notes for Lecture 13 on the electric dipole field The magnetic dipole moment is defined by 1 m apr39r39 X Jr39 1 with the corresponding potential to m X f p A 7 2 r 4W 7 2 and i39nagnetostatic field 7 p0 3fmf m 8W A3 Br g 7 3 7 139 The last term of the field expression follows from the following derivation We note that Eq is poorly defined 7 gt 0 and consider the value of a small integral of Br about zero For this purpose we are supposing that the dipole m is located at r O In this case we will approxii39nate Br z 0 z Brd3r 531 4 sphere First we note that Brd3r R2 f x Ar d0 5 TSR TR This result follows from the divergence theori n m v Vd3r umixm 6 In our case this theorem can be used to prove Eq 5 for each cartesian coordinate of V X A since V X A V X A 5 5r V X A 2 2 V X Note that 5 V X A V 2 X A and that we can use the Divergence theorem with V E 2 X Ar for the x coi nponent for example v it x Ami it x A fdA A x f 5dA 7 v0 surface surface Therefore v x Am A x f 592 yy 2mm R2 i x AdQ 8 TSR TR T R Which is identical to Eq Now expressing the vector potential in terms of the current densitv Lo 3 J 1quot Ar 4Wdlrrll 9 we can use the identity I 4W rlt A 527 if 10 d r r 3amp1 Therefore 2 A Hz f X AdQ W 0137quot 4 r x Jm 11 rhz 3 If the sphere R contains the entire current distribution then rgt R and rlt 7quot so that 11 becoi nes 4 8 R2 f x AMQ g 137quot r39 x Jr E gm 12 TI

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