### PHYSICS FOR IITJEE

MECHANICS
MOTION IN ONE DIMENSION
Graphs
PROJECTILE MOTION
NEWTON LAWS OF MOTION
Tension
FRICTION
Friction
CONSERVATION LAWS
Collision
CIRCULAR MOTION
CENTRE OF MASS
VARIABLE MASS SYSTEMS
GRAVITATION
Gravitation
RIGID BODY DYNAMICS
ELASTIC PROPERTIES OF MATTER
FLUID DYNAMICS
Viscosity
SIMPLE HARMONIC MOTION
ELECTRICITY AND MAGNETISM
GAUSS LAW OF ELECTROSTATICS AND APPLICATIONS
Capacitance
POLARIZATION OF DIELECTRICS
WORK AND ENERGY IN ELECTROSTATICS
CURRENT ELECTRICITY
MAGNETOSTATICS
Ampere Law
MAGNETIC MATERIALS
DC CIRCUITS
RC Circuit
LR circuit
LC Circuit
AC CIRCUITS
AC Circuit
OPTICS
Waves
Thin Lens
THERMAL EXPANSION
CALORIMETRY
Calorimetry
TRANSMISSION OF HEAT
FIRST LAW OF THERMODYNAMICS
SECOND LAW OF THERMODYNAMICS
MODERN PHYSICS

# Coulomb’s Law

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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 $q_2$.