1. EEE 340Lecture 041 2-4.3 Spherical Coordinates

2. EEE 340Lecture 042 A vector in spherical coordinates The local base vectors from a right –handed system

3. EEE 340Lecture 043 The differential length The differential areas are The differential volume

4. EEE 340Lecture 044 On many occasions the differential areas are vectors

5. EEE 340Lecture 045 Table 2-1 Basic Orthogonal Coordinates Cartesian Cylindrical Spherical

6. EEE 340Lecture 046 Cartesian coordinates and are vectors. is a scalar. Differential displacement Differential normal area Differential volume

7. EEE 340Lecture 047 The differential surface element may be defined as we need to remember only !

8. EEE 340Lecture 048 Cylindrical coordinates Differential volume Differential normal area Differential displacement

9. EEE 340Lecture 049 Coordinate transforms Example 2-11. Convert a vector in spherical coordinates (SPC) into the Cartesian coordinates (CRT). Solution. The general form of a vector in the CRT is We need In fact

10. EEE 340Lecture 0410 The other eight dot-products can be worked out. A faster and better way to represent the transformation is based on the del operator.

11. EEE 340Lecture 0411 Example 2-12 Sphare chell r a =2 cm r b =5 cm The charge density Find the total charge Q

12. EEE 340Lecture 0412 Solution:

13. EEE 340Lecture 0413 2-5 Integrals Containing Vector Functions.

14. EEE 340Lecture 0414 The line integral around a close path C is denoted as In the Cartesian coordinates (CRT)

15. EEE 340Lecture 0415 Example 2-13 a) along the straight line OP, where P(1,1,0) P(1,1,0) y x 0 P1P1 P2P2

16. EEE 340Lecture 0416 b). Along path OP 1 P Solution. Using (2-52) of cylindrical a).