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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
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FAQs on Short Notes: Vector Analysis - Short Notes for Electrical Engineering - Electrical Engineering (EE)

1. What is vector analysis in electrical engineering?
Ans. Vector analysis in electrical engineering is a mathematical tool used to analyze and solve problems related to electrical circuits and electromagnetic fields. It involves the use of vectors to represent physical quantities such as electric fields, magnetic fields, and currents.
2. How is vector addition used in electrical engineering?
Ans. Vector addition is used in electrical engineering to combine multiple vectors representing different physical quantities, such as electric fields or currents. By adding these vectors together, engineers can determine the overall effect or result of the combined quantities.
3. What is the significance of the dot product in vector analysis for electrical engineering?
Ans. The dot product in vector analysis is significant in electrical engineering as it allows engineers to calculate the magnitude of a vector projection onto another vector. This is useful in determining the component of a vector in a specific direction, such as finding the work done by a force in a given direction.
4. How do engineers use cross products in vector analysis for electrical engineering applications?
Ans. Engineers use cross products in vector analysis to calculate the magnitude and direction of a vector that is perpendicular to two given vectors. This is essential in determining the orientation of electromagnetic fields or forces in electrical systems.
5. Can vector analysis be applied to circuit analysis in electrical engineering?
Ans. Yes, vector analysis can be applied to circuit analysis in electrical engineering to analyze complex circuits with multiple components and varying currents. By representing circuit elements as vectors, engineers can simplify the analysis and solve circuit problems efficiently.
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