<<  Previous    answermath HOME   answermath en Español       Loan Calculator Find any Print, Poster Next >>    
  Electromagnetism: Fields ▫ Electricity ▫ Magnetism ▫ Induction     Artificial Intelligence Tutorials: Data Mining Neural Networks Fuzzy Logic Genetic Algorithms    
  Practice on line: Addition Subtraction  Multiplication Division Root Exponentiation Sine Cosine Tangent Fuzzy   Mental math Tips: Addition ▫ Subtraction Multiplication Division Sine Cosine Tangent  
       
 

ELECTROMAGNETIC FIELDS AND THEORY: FIELDS AND VECTORS: Cylindrical Coordinates 

 

1.2.2 Cylindrical

Another system, as indicated in figure [3], here a point P can be identified by using coordinates

rp , φp , zp  (10)

 

 
     
 

       
   


the unitary vectors that indicate the direction in which the coordinates grow are,

(11)

Now, the unitary directions aren’t constant in all the points, only coordinate z will always grow in the same direction. The directions will be so that,


(12)

the differential displacements along the above directions will be,
dr , r dφ , dz  (13)

a generic displacement for point P,

     
(14)

In figure [4], a differential volume element is shown as well as the differential elements of area that enclose it. The differential element of volume is equal to,


dV = r dr dφ dz  (15)

 



the faces perpendicular to direction z have a differential area equal to,


dSz = r dφ dr  (16)

The area of the faces perpendicular to direction r,

dSr = r dφ dz  (17)

and the area of the faces perpendicular to direction φ,

dSφ = dr dz  (18)

Also, in this system of coordinates, any element of area can be expressed through a vector with a magnitude equal to the area and with a direction perpendicular to the element.


 

 
     
Google
  Web http://www.answermath.com
   
 
 

| Home | Suggest a link  | Send Comments  | Disclaimer | PrivacyPolicy | Links | Help |

Copyright 2000 - wgonz @ email.com - All  Rights   Reserved