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Coulomb’s Law

If two stationary and point charges Q1 and Q2 are kept at a distance r (Fig. 2), then it is found that force of attraction or repulsion between them is
i.e., 37164.png(k = proportionality constant)
Fig. 2
In C.G.S. (for air), k = 1, 37176.png Dyne
In S.I. (for air), 37182.png
⇒ 37190.png N (1 N = 105 Dyne)
ε0 = Absolute permittivity of air or free space = 37203.png. Its dimensional formula is 37209.png

Vector form of coulomb’s law

Vector form of Coulomb’s law is
where 37226.png is the unit vector from first charge to second charge along the line joining the two charges.

Effect of medium

When a dielectric medium is completely filled in between charges, rearrangement of the charges inside the dielectric medium takes place and the force between the same two charges decreases by a factor of K (dielectric constant).
i.e., 37232.png
Here ε0 K = ε0 εr = ε = permittivity of medium.

Principle of superposition

According to the principle of superposition, total force acting on a given charge due to number of charges is the vector sum of the individual forces acting on that charge due to all the charges.
Fig. 3
Consider number of charges Q1, Q2, Q3, ... are applying force on a charge Q.
Net force on Q will be 37293.png
Some Important Notes
  • ε0 = Absolute permittivity of air or free space = 37377.png. Its dimension is 37383.png.
  • ε0 Relates with absolute magnetic permeability (μ0) and velocity of light (c) according to the following relation 37389.png.
  • Coulomb’s law is not valid for moving charges because moving charges produces magnetic field also.
  • Coulomb’s law is valid at a distance greater than 10–15 m.
  • A charge Q1 exerts some force on a second charge Q2. If third charge Q3 is brought near, the force of Q1 exerted on Q2 remains unchanged.
  • Ratio of gravitational force and electrostatic force between
    1. two electrons is 10–43/1,
    2. two protons is 10–36/1, and
    3. one proton and one electron 10–39/1.
  • Decreasing order to fundamental forces37395.png

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