Formula Sheet PDF

Preview

Summary

Formula Sheet...

Description

Formula Sheet 2 – Additional Formulae to Those Given In the Inside Cover of Griffiths (When quoting formulae from this sheet, write down the formula and its number) 1. DEFINITIONS    



(1.3)



∑ 

,

2

4

ˆ 12

(2.1)

1 4

 

∑

 

4

35

∫

ˆ

4

(2.4)

ˆ

(2.5)



2







(2.6)

0

0

 

0



∫





 



(2.7)



3 /8

1 1

(3.1)

3

5

5

63

∫

3

(3.2)

3 /2 5

70

3

15 / 8



cos

(3.3)



  

 ...  

ˆ 2



(3.4)



∫









(3.5)

1

1 3

4

 3 .ˆ ˆ



(3.6)

0

4. STATIC ELECTRIC FIELDS IN MATTER





2

0

0

∑

0



cos

1

0



0

4





 

30

∑

4

0

∫

4

1

(2.3)

ˆ



1 /2

1

2

  

For an arbitrary charge distribution at the origin:



2

∫

1

 

(2.2)



1

 

ˆ

0

4

∫

3



1 4

2

1

0

(2.17)

1 2

2

0

 

∫

2 2

  1

1

0

1

 

 0

2. ELECTROSTATICS 1

2

3. SPECIAL TECHNIQUES

(1.2)





1 2

W

(1.1)

 



0

C





(2.8)

(4.1)







2

(2.9) 0



1 4



∑



  

(4.2) (4.3)

 

(2.10)

∫

(4.4)



 



  

(2.11)

0

ˆ

(4.5) (4.6)



1

∫

4

 

(2.12)

4

 



(4.7)

0

0



1







4



1

0

1





∫

∫

(2.13)

 





 



0

 ,

1

,

 1

2

,

1



2

,



(4.9)

2





0

1

(2.14)

1 4 1 2∫

∑∑ 0

1





1 ∑ 2 1 0

2

∫



2



(2.16)

1 2

1

∫

0

   

(4.10) (4.11)

  0

2

2

0

   

1



(2.15)

(4.8)

1

  (for linear dielectric)

(4.12) (4.13)

5. MAGNETOSTATICS 





 







  

(5.2)



∫ ∫

 (5.1)

∫



6. STATIC MAGNETIC FIELDS IN MATTER





(6.1)

(5.3)

 





  

(6.4)

 



(6.5)

 

(6.6)

4

4  

ˆ



 

  0

  

0  

  0

∫

0

4

0

(5.12)

∫

(Coulomb gauge)

(5.15)

 

(

(5.16)

"

)

4

∫

"

(

1



,

2

 2

"

)

(5.17)

4

1

∑

0  4  



1

0

∫

0

"

"

)

2



 

,

∑

1

(5.18)

0

(5.19)

ˆ2

(5.20)

1

  ,

0 1

1

4

∫∫

,

(7.5) 1

(7.6)

∫



2

(7.7)

0

  

 ,



,

 

  ,

,

0

 



cos

(7.4)



1

2

1

(5.21)

ˆ

(7.3)



1 2

For an arbitrary current distribution at the origin: 0







1

(7.1)

1

(

(6.11)





2 ,

 

1

(7.2)

(5.14)

"

0



∫

∫

0

1

(6.9)

1

 

(5.13)



 

,

(6.8)

ˆ2

 

1

∫

0

4

2

7. ELECTRODYNAMICS

 

 

(6.7)



0



 









 



(5.11)

2

0





,

2

(5.10)



∫   ∫

2





ˆ 2

∫

0

,

 

(6.10)



 

(5.9)

2

∫

0

1

1

ˆ  

 



(5.8)



∫

4



,

,

 0

 

∫

(5.7)

,

 

 

ˆ

0



  

 

 

(5.6)







 

(5.5)



 

(6.3)



(5.4)



2

(6.2)

 







 ,

0

 

,

 0

,

  , 0 0

(7.8)

 ...  (5.22)

2...