# Fundamental Concepts of Electromagnetism

E = 1/4πε0 q/r2

where E = Electric potential energy, energy of electric field or intensity of electric field

q          = charge place at distance r from infinitesimal test charge

r           = distance between point charge and infinitesimal charge

ε0         = permittivity of free space

= 8.854 x 10-12 Coul2/ Newton-met2

2.   D= ε0E +P

where D = displacement vector

P= polarization vector (electric dipole moment per unit volume )

P = n (q r) V

where              n = number of term

V= volume

q r = electric dipole moment

3. Φ= B.A

where Φ= magnetic flux

B= magnetic intensity

A= area

B= Φ/ A= Weber/met2

4.  F = i B l sin θ.,     is Lorentz force.

where F= The magnetic force on the conductor

i =current in magnetic field

l= whole length of the conductor

B= uniform field of conduction

from above equation

B=F/il = Newton / Amp * met  = Tesla

1 Tesla = 104 Gauss

5. Biot-Savart’s Law

B  =µ0 /4π i∆ l sin θ/ r2

where µ0 = permeability of free space

6. B =µ0 H

where H = magnetising force

7. B =  µ0 (M+H)

where M = magnetic intensity

H = intensity of magnetisation or magnetic moment per unit volume

8 .A =  IA x +Ja y + Ka z

B =IBX +JBY =KBZ

(i) A.B =AX BX + AY BY+AZ BZ

(ii)A X B         I           j           K

AX       AY          AZ

BX        BY        BZ

(iii) A .(B XC) =(A.C) B- (A.B) .C

(iv) A X (BXC) =(A.C) .B –(A.B) .C

9. ∆=del operator

10. Gauss Transformation Formula

If any volume V is enclosed by the surface S then surface integral can be changed into volume integral by Gauss transformation formula in the following manner

N .B (i) curl (grad ϕ) =0

And (ii) div (cual A)  =0

11. Stoke’s Transformation Formula

By this transformation we change line integral into surface integral

Applying Gauss transformation

p = charge per unit volume or charge density

This is the continuity equation.