Coulomb's law is an
experimental law formulated in 1785 by the French colonel, Charles Augustin de
Coulomb. It deals with the force a point charge exerts on another point charge.
By a point charge we mean a charge that is located on a body whose dimensions
are much smaller than other relevant dimensions. For example, a collection of
electric charges on a pinhead may be regarded as a point charge. Charges are
generally measured in coulombs (C). One coulomb is approximately equivalent to
6 X 10

^{18 }electrons; it is a very large unit of charge because one electron charge e = -1.60 X 10^{-19}C.
Coulomb's law states that
the force between two point charges Q

_{1}and Q_{2}is:
a) Along the line joining
them

b) Directly proportional to
the product Q

_{1}Q_{2}of the charges
c) Inversely proportional to
the square of the distance R between them.

Mathematically we can write
as below.

F = kQ

_{1}Q_{2}/ R^{2}……………………(1)
where k is the
proportionality constant. In SI units, charges Q

_{1}and Q_{2}are in coulombs (C), the distance R is in meters (m), and the force F is in newtons (N) so that k = 1/4πξ_{0}. The constant so is known as the permittivity of free space (in farads per meter) and has the value
ξ

_{0}= 8.854x10^{-12}= 10^{-9}/ 36π F/m
and k = 1/4πξ

_{0}= 9x10^{9}m/F
Thus from equation (1), we
can write as

F = (Q

_{1}Q_{2}) / 4πξ_{0}R^{2}
If point charges Q

_{1}and Q_{2}are located at points having position vectors**r**and_{1}**r**, then the force_{2}**F**on Q_{12}_{2}due to Q_{1}, shown in figure below, is given by**F**= [(Q

_{12}_{1}Q

_{2}) / 4πξ

_{0}R

^{2}]

**a**…………………(2)

_{R12}
Where

**a**is unit vector in the direction of force experienced by charge Q_{R12}_{2}by Q_{1}.
Here,

**R**=_{12}**r**–_{2}**r**and R is the magnitude of vector_{1}**R**._{12}
Therefore, unit vector in
the direction of

**R**,_{12}**a**=

_{R12}**R**/ R

_{12}
Therefore from equation (2),
force

**F**on Q_{12}_{2}due to Q_{1}_{}

**F**= [(Q

_{12}_{1}Q

_{2}) / 4πξ

_{0}R

^{2}]

**a**

_{R12}**⇒**

**F**= [(Q

_{12}_{1}Q

_{2}) / 4πξ

_{0}R

^{3}]

**R**

_{12}

_{}
= [(Q

_{1}Q_{2}) / 4πξ_{0}R^{3}] (**r**–_{2}**r**)_{1}**Some important points about Columb’s Law:**

a) It shall be noted that from
the figure above that, the force

**F**, on Q_{21}_{1}due to Q_{2}is given by,**F**= F

_{21}_{12}

**a**= F

_{R21}_{12}(-

**a**)

_{R12}**⇒**

**F**= -

_{21}**F**

_{12}
Like charges (charges of the
same sign) repel each other while unlike charges attract as shown in figure
below.

b) The distance R between the
charged bodies Q

_{1}and Q_{2}must be large compared with the linear dimensions of the bodies; that is, Q_{1}and Q_{2}must be point charges.
c) Q

_{1 }and Q_{2}must be static i.e. at rest.
d) If we have more than two
point charges, we can use the principle of superposition to determine the force
on a particular charge. The principle states that if there are N charges Q

_{1}, Q_{2},……,Q_{N}located, respectively, at points with position vectors**r**,_{1}**r**,. . .,_{2}**r**then resultant force F on a charge Q located at point r is the vector sum of the forces exerted on Q by each of the charges Q_{N}_{1}, Q_{2},. . ., Q_{N}. Therefore,
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