Short Notes: Vector Analysis | Short Notes for Electrical Engineering - Electrical Engineering (EE) PDF Download

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     In communication systems, circuit theory is valid at both the transmitting end as well as 
the receiving end but it fails to explain the flow between the transmitter and receiver. 
 
     Circuit theory deals with only two variables that is voltage and current whereas 
Electromagnetic theory deals with many variables like electric field intensity, magnetic field 
intensity etc., 
 
       Mostly three space variables are involved in electromagnetic field problems.  Hence the 
solution becomes complex.  For solving field problems we need strong background of vector 
analysis. 
  
       Maxwell has applied vectors to Gauss’s law, Biot Savart’s law, Ampere’s Law and 
Faraday’s Law.  His application of vectors to basic laws, produced a subject called “Field 
Theory”.   
 
 
2. Scalar and Vector Products  
   
a) Dot Product: is also called scalar product. Let ‘ ?’ be the angle between vectors 
A and B. 
 
 
     
 
  A . B  = | A |  | B | cos ? 
 The result of dot product is a scalar.  Dot product of force and distance gives work done (or)  
            Energy which is scalar.                                                      
             a
n
 
b) Cross product:  is also called vector product. 
 
                                                                                            B 
                                 A x  B = |A| | B| sin ? â
n
             
                                                                                                                          A 
  
                  S = |S| â
n
         where |S| = |A| |B| Sin ?  
 
To find the direction of S, consider a right threaded screw being rotated from A to B. i.e. 
perpendicular to the plane containing the vectors A and B. 
            
                   ? A x B = - (B x A) 
 
 3. Operator Del ( ?  ):  
 Del is a vector three dimensional partial differential operator.  It is defined in Cartesian 
system as 
 
                         ?  =      ?    i   +      ?       
j   
+     ?    
 k
 
    ?x              ?y                ?z    
                      
 
 
 Del is a very important operator.  There are 3 possible operations with del. They are gradient, 
divergence and curl. 
     (Contd….2) 
VECTOR ANALYSIS