### ELECTRICITY AND MAGNETISM FOR IIT JAM

COULOMB LAW AND ELECTRIC FIELD
GAUSS LAW OF ELECTROSTATICS AND APPLICATIONS
Capacitance
POLARIZATION OF DIELECTRICS
Capacitors
WORK AND ENERGY IN ELECTROSTATICS
BOUNDARY VALUE PROBLEMS
CURRENT ELECTRICITY
MAGNETOSTATICS
Ampere Law
MAGNETIC MATERIALS
DC CIRCUITS
RC Circuit
LR circuit
LC Circuit
AC CIRCUITS
AC Circuit
MAXWELL EQUATIONS
POYNTING VECTOR
ELECTROMAGNETIC WAVES
REFLECTION AND REFRACTION OF EM WAVES AT THE INTERFACE OF TWO DIELECTRICS

# Coulomb’s Law

Force between two point charges (interaction force) is directly proportional to the product of magnitude of charges ($q_1$ and $q_2$) and is inversely proportional to the square of the distance between them i.e., $\left ( 1/r^2 \right )$. This force is conservative in nature. This law is also called inverse square law. The direction of force is always along the line joining the point charges.

$F \propto \dfrac{q_1 q_2}{r^2}$ $F = k \dfrac{q_1 q_2}{r^2}$ $k = \dfrac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 N-m^2/C^2$ $\varepsilon_0 = \mathrm{permittivity \ of \ free \ space} = 10^{-12} C^2/ N-m^2$

Coulomb’s Law in Vector Form

Suppose the position vectors of two charges $q_1$ and $q_2$ are $\bar{r}_1$ and $\bar{r}_2$, then, electric force on charge $q_1$ due to charge $q_2$ is,

$\bar{F}_{12} = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{q_1 q_2}{|\bar r_1 - \bar r_2 |^3} \left ( \vec {r_1} - \vec{r_2} \right)$

Similarly, electric force on $q_2$ due to charge $q_1$ is

$\vec F_{12} \dfrac{1}{4 \pi \varepsilon_0} \dfrac{q_1 q_2}{|\bar r_2 - \bar r_1|^3} \left ( \bar r_2 - \bar r_1 \right )$

Here $q_1$ and $q_2$ are to be substituted with sign. Position vector of charges $q_1$ and $q_2$ are and respectively where $(x_1 y_1 z_1)$ and $(x_2 y_2 z_2)$ are the coordinates of charges $q_1$ and $q_2$.