griffiths 5 22 - physics & astronomyhomepage.physics.uiowa.edu/~rmerlino/129fall12/griffiths...

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Griffiths 5.22 (Magnetic vector potential for a finite wire) 2 1 2 2 2 2 2 2 2 2 1 1 12 12 2 2 2 2 2 1 2 2 2 2 2 2 1 1 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ˆ ˆ () ln 4 4 4 ˆ ˆ 4 4 z o o o z o z o z s z I I I dl dz Ar z z s z z s z ss z ss z I A B A s z s z z s z ss z z s z I B z s z z s z r 12 2 2 2 2 1 1 1 2 2 2 2 1 1 1 1 2 1 2 2 2 2 2 1 ˆ ˆ 4 o ss z z s z z s z z s z I z z B s s z s z 2 1 ˆ sin sin 4 o I B s z dl s r z z 1 z 2 dA r = s 2 + z 2 s z 1 z 2

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Page 1: Griffiths 5 22 - Physics & Astronomyhomepage.physics.uiowa.edu/~rmerlino/129Fall12/Griffiths 5_22.pdf · Griffiths 5.22 (Magnetic vector potential for a finite wire) 2 1 22 22 22

Griffiths 5.22 (Magnetic vector potential for a finite wire)

2

1

2 22 2

2 2 2 21 1

1 2 1 22 2 2 22 1

2 2 2 22 2 1 1

1 22 2 2 22 2 2

2 2 2 22 2 2 2

ˆ ˆ( ) ln4 4 4

ˆ ˆ4

4

z

o o o

z

oz

o

z s zI I Idl dzA r z z

s z z s z

s s z s s zIAB A

s z s z z s z

s s z z s zIB

z s z z s z

r

1 22 2 2 21 1 1

2 2 2 21 1 1 1

2 1

2 2 2 22 1

ˆ

ˆ4

o

s s z z s z

z s z z s z

I z zB

s s z s z

2 1 ˆsin sin

4o IBs

zdl

s r

z

z1 z2

dA r = s2 + z2

s

z1 z2