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Coluomb’s law

We know that two charged bodies  either attract or repel each other. Like charges repel each others and unlike charges attract each others.  Coulomb’s Law attempts to define the force that is exerted when the two bodies are attracted or repelled because of their charges.


Coulomb’s Law states that:


The force exerted between two stationary point charges:


i. Is directly proportional to the product of charge strength of the two charges.


ii. Is inversely proportional to the square of distance between the two charges.


Mathematically the Coulomb’s law can be represented as:
F \propto Q_1 \times Q_2 \;\;\;\; ..i                   and                        F \propto \frac{1}{r^2} \;\;\;\; ..ii


Where, F = Force of attraction between the two particles ,Q1 = charge of first particle , Q2 = charge of second particle and r = distance between the two particles.


Combining equation i and ii we get:
F \propto \dfrac{Q_1 \times Q_2}{r^2}


Now if we replace the proportionality by the constant of proportionality (K ) then we get:


F = K \times \dfrac{Q_1 \times Q_2}{r^2}


The constant of proportionality (K ) is called the Dielectric Constant and given as :


K = K_e \times \frac{1}{\epsilon_r}
Where, K_e Is the Coulomb’s constant or electrostatic constant and


\epsilon _r = relative Permittivity.


The Value of Coulomb’s Constant is:


K_e = \dfrac{1}{4 \pi . \epsilon _0} ,                   Where, \epsilon _0 = Permittivity of vacuum.


Thus, The final formula of  Coulomb’s Law after we place the value of constant of proportionality (K ) can be summarized as following:


F = \dfrac{Q_1 \times Q_2}{4 \pi \epsilon_0 \epsilon_r r^2}


And the exact value of Coulomb’s Constant is:
K_e = \dfrac{1}{4 \pi 8.854 \times 10 ^{-12}} = 8.9875 \times 10^9 N.m^2.C^{-2}


Coulomb’s Law is valid only under following circumstances:


a. The two charged bodies should be  a point charge.


b. The two charged points should be stationary with respective to each others.

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