Monday, August 30, 2010

Electro Magnetic Fields(EEE 2-1)R09


              Electromagnetic Fields

Unit-1                      Electrostatics
Unit-2                      Conductors and Dipole
Unit-3                      Dielectric & Capacitance
Unit-4                      Magneto statics
Unit-5                      Ampere’s circuit law & its applications
Unit-6                      Force in Magnetic fields
Unit-7                      Magnetic potential
Unit-8                      Time varying fields
                       









                                   Unit-1      ELECTROSTATICS


Coulomb’s law:
Coulomb’s law states that the force ‘F’ between two point charges Q1 & Q2 is directly proportional to the product of two charges and inversely proportional to the square of the distance ‘R’ between them and is along the line joining them.
                                    F = K.Q1.Q2 / R2
Where ‘K’ is a proportionality constant  whose value depends on the system of units.
Q1 & Q2 are in coulomb’s(c),  ‘R’ is the distance in meters(m) and force in ‘N’.
                                     K = 
Where ε0 is called the permittivity of free space and             Q1
       ε0 = 8.85* 10-12  F/m         or              K=    = 9*109  m/F        r1         R
                                    F =  . Q1.Q2/ R2                        Q2
r2
If point charges Q1 & Q2 are located at points having position vectors      o
r1 & r2 then the force F12 = Q1.Q2.ar12 / 4πε0.R2
Where  R12 = r2 – r1    ;                       R = |R12|          ;           ar12 = R12/ R
                        F12  = Q1.Q2(r2-r1)/ 4πε0|r2-r1|3        
Similarly force F12 on Q1 due to Q2 , which is same in magnitude but opposite in direction, i.e,
 F21 = -F12     ;    F21 = |F12|ar21 = |F12|(-ar12)        i.e.,   ar21 = -ar12
Coulomb’s law of point charges is applicable when the distance ‘R’ between Q1 & Q2 must be large when compared to linear dimensions of the charges i.e. Q1 & Q2 must be point charges.
If there are more than two point charges i.e. if there are ‘N’ charges then the principle of superposition of charges is applied. It states that if there are ‘N’ charges Q1,Q2,……Qn located at positions r1,r2,…….rn, then the resultant force ‘F’ is given by , sum of the forces exerted on Q be each of the charges Q1,Q2,…….Qn.
F =  
Electric field intensity (EFI):
                        It is defined as the force per unit charge when placed in an electric field.
                                      E = F/Q
For Q>0 , the electric field intensity ‘E’ is obviously in the direction of the force ‘F’ and is measured in newtons per coulomb or  volts per meter. The electric field intensity at a point ‘r’ due to a point charge located at ‘r|’ is given by
                                    E = Q.ar / 4πε0.R2    =  Q(r-r1)/ 4πε0(r-r1)3
Similarly for N charges , the electric field intensity at ‘r’ is given by ,
                        E =  
Electric fields due to charge distributions:
Line charge:
                                    Fig-1:
            Consider a line charge with uniform charge density ‘ρL’ extending from A to B along the Z-axis . The charge dQ associated with    dl = dz  of the line is   dQ = ρL.dl= ρL.dz
& hence total charge Q is   Q =  
The electric field intensity E at an arbitrary point P(x,y,z) can be found using
                        E =    
From fig.                                 dl = dz1
                        R = (x,y,z)-(0,0,z1)  = xax +yay +(z-z1)az      or     R = ρ.aρ  + (z-z1)az
           R2  = |R2| = x2 + y2 + (z-z1)2 = ρ2 + (z-z1)2  
            ar/R2 = R/|R|3 = (ρ.aρ+(z-z1)az)/(ρ2+(z-z1)2)3/2 
E = ρL   dz1
                R = 

1 comment:

  1. D: Looks pretty complicated. My head is now full of F**k.

    ReplyDelete