Classical Electrodynamics

1. 1
Given point (-2,6,3) and vector
( ) , express
in cylindrical and spherical
coordinates. Evaluate in the
Cartesian, cylindrical, and spherical
systems.
x y
P
y x z P and
at P
  
A a a
A
A
Solution

2. 2

3. 3
2 2
2 2
2, 6, 3
( 2) 6 40
2 10 2 3.16
6.32
Given
x y z
x y
X

   
  
   
 


4. 4
1 1
1 0
0
2, 6, 3
6
tan tan
2
tan ( 3) 108
{ 180 72 108}
( , , ) (6.32,108 ,3)
Given
x y z
y
x
z

 
 

   
  

  
 
 
2 2 2
2, 6, 3
4 36 9 49 7
Given
x y z
r x y z
   
   
    

5. 5
2 2
1
1
1 0
2, 6, 3
tan
40
tan
3
tan 2.11 65
Given
x y z
x y
z
 


   

 

 

6. 6
2 2
1
1
1 0
0 0
2, 6, 3
tan
40
tan
3
tan 2.11 65
( , , ) (7,65 ,108 )
Given
x y z
x y
z
r

 



   

 

 
 