Coulomb’s Law in Electrostatics | Force Between Point Charges (GATE ECE EMFT)

Coulomb’s Law Statement

Do point charges ke beech force directly proportional hoti hai unke product ke aur inversely proportional hoti hai distance ke square ke.

$$ F \propto \frac{q_1 q_2}{r^2} $$

Final Formula:

$$ F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2} $$

Key Points:

• Force line joining charges ke along act karti hai
• Like charges → repulsion
• Unlike charges → attraction
• Inverse square law follow hota hai

Vector Form of Coulomb’s Law

Force ek vector quantity hai, isliye direction important hota hai.

$$ \vec{F}_{12} = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}\hat{r}_{12} $$

Meaning:

• ĥr₁₂ direction show karta hai
• Force always line joining charges ke along hoti hai

Effect of Medium (Permittivity)

Medium change hone par force decrease hoti hai due to permittivity.

$$ F = \frac{1}{4\pi\varepsilon}\frac{q_1 q_2}{r^2} $$

Where:

• ε = permittivity of medium
• ε₀ = permittivity of free space
• ε = ε₀εr

Superposition Principle

Multiple charges hone par net force individual forces ka vector sum hota hai.

$$ \vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \cdots $$

Key Points:

• Forces vector form me add hote hain
• Direction consider karna mandatory hai

Nature of Force

Coulomb’s Law vs Gravitational Law

GATE Level Insights

• Vector direction is most important
• Superposition frequently asked
• Dielectric medium concepts common
• Multi-charge systems are standard questions

Common Mistakes

• Scalar addition instead of vector addition
• Wrong direction of force
• Ignoring permittivity of medium
• Sign confusion in charges

Final Summary

Coulomb’s Law electrostatics ka base hai jo charge interaction define karta hai aur EMFT ke sabhi advanced topics ki foundation hai.

$$ F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2} $$