Question

State Coulomb&rsquo;s law in electrostatics. Express it in SI units. Mention two similarities and two dissimilarities between electrostatic and gravitational interactions.

Accepted Answer

Coulomb's law for electrostatics:-

According to Coulomb's law " The electrostatic force of attraction or repulsion between two charges separated by certain distance is

$(I)$ Directly proportional to the product of magnitude of two point charges

$i . e . F \propto q_{1} q_{2}$

and $(II)$ Inversely proportional to the square of separation between them.

$i . e . F \propto \frac{1}{r^{2}}$

$\Rightarrow F \propto \frac{q_{1} q_{2}}{r^{2}} \Rightarrow F = K \frac{q_{1} q_{2}}{r^{2}}$

where $K$ is constant of proportionality having value $k = \frac{1}{4 π ϵ}$

where $ε =$ Permittivity of medium and $ϵ = ϵ_{0} \cdot ϵ_{r}$

where $ε_{0} =$ Permittivity of vacuum and $ε_{r} =$ Relative Permittivity

$K =$ Dielectric constant having value $1$ for vacuum or air or free space.

$\Rightarrow F = \frac{1}{4 π ϵ} \cdot \frac{q_{1} q_{2}}{r^{2}} = \frac{1}{4 π ϵ_{0} \cdot ϵ_{r}} \cdot \frac{q_{1} q_{2}}{r^{2}} = \frac{1}{4 π ϵ_{0}} \cdot \frac{q_{1} q_{2}}{r^{2}}$ for vacuum or air

$\Rightarrow F = 9 \times 10^{9} \frac{q_{1} q_{2}}{r^{2}}$

Similarity between electrostatics and gravitational interaction

(I) Both forces are proportional to a property which represents the strength of interaction for a given field.

As electrostatic force is proportional to magnitude of the charges of interacting objects and gravitational force is proportional to the masses of interacting objects.

(ii) Both forces are acted along the line joining two objects processing with masses and charges. So they are central and conservative forces.

Dissimilarities between gravitational and electrostatic interaction:-

Electrostatic forces are stronger than gravitational forces.

Electrostatic forces are attractive and repulsive both whereas the gravitational force is only attractive.

State Coulomb’s law in electrostatics. Express it in SI units. Mention two similarities and two dissimilarities between electrostatic and gravitational interactions.

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