Basic Properties of Electric Charges and Coulomb\'s Law
− Absolute permittivity of free space = 8.854 × 10−12 C2 N−1 m−2
− Unit vector pointing from charge q1 to q2
− Unit vector pointing from charge q2 to q1
[
is along the direction of unit vector 
] …(ii)
[is along the direction of unit vector] …(iii)
Basic Properties of Electric Charges
- Additive nature of charges − The total electric charge on an object is equal to the algebraic sum of all the electric charges distributed on the different parts of the object. If q1, q2, q3, … are electric charges present on different parts of an object, then total electric charge on the object, q = q1 + q2 + q3 + …
- Charge is conserved − When an isolated system consists of many charged bodies within it, due to interaction among these bodies, charges may get redistributed. However, it is found that the total charge of the isolated system is always conserved.
- Quantization of charge − All observable charges are always some integral multiple of elementary charge, e (= ± 1.6 × 10−19 C). This is known as quantization of charge.
Coulomb’s Law
- Two point charges attract or repel each other with a force which is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Where, 
[In SI, when the two charges are located in vacuum]
[In SI, when the two charges are located in vacuum]− Absolute permittivity of free space = 8.854 × 10−12 C2 N−1 m−2
We can write equation (i) as
- The force between two charges q1 and q2 located at a distance r in a medium may be expressed as
Where 
− Absolute permittivity of the medium
− Absolute permittivity of the medium
The ratio 
is denoted by εr, which is called relative permittivity of the medium with respect to vacuum. It is also denoted by k, called dielectric constant of the medium.
is denoted by εr, which is called relative permittivity of the medium with respect to vacuum. It is also denoted by k, called dielectric constant of the medium.
ε = kε0
Coulomb’s Law in Vector Form
Consider two like charges q1 and q2 present at points A and B in vacuum at a distance r apart.
According to Coulomb’s law, the magnitude of force on charge q1 due to q2 (or on charge q2 due to q1) is given by,
Let
− Unit vector pointing from charge q1 to q2− Unit vector pointing from charge q2 to q1 [is along the direction of unit vector ] …(ii)[is along the direction of unit vector] …(iii)
∴Equation (ii) becomes
On comparing equation (iii) with equation (iv), we obtain
Forces between Multiple Charges
Principle of superposition − Force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual forces are unaffected due to the presence of other charges.
Consider that n point charges q1, q2, q3, … qn are distributed in space in a discrete manner. The charges are interacting with each other. Let the charges q2, q3, … qn exert forces 
on charge q1. Then, according to principle of superposition, the total force on charge q1 is given by,
on charge q1. Then, according to principle of superposition, the total force on charge q1 is given by,
If the distance between the charges q1 and q2 is denoted as r12; and is unit vector from charge q2 to q1, then
is unit vector from charge q2 to q1, then
Similarly, the force on charge q1 due to other charges is given by,
Substituting these in equation (i),
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