Coulomb’s Law of Electric Force

At the heart of understanding electric forces is Coulomb’s Law, which describes the interaction between charged particles. Electricity is one of the fundamental forces of nature that governs countless phenomena around us. Named after the French physicist Charles-Augustin de Coulomb, this law plays a crucial role in the study of electrostatics.

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What is Coulomb’s Law?

Coulomb’s Law states that:

The magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Mathematically, it can be expressed as:

\boxed{F = k \frac{{|q_1 \cdot q_2|}}{{r^2}}}

Where:

• F = Force between the charges (in Newtons, N)
• q₁ and q₂ = Magnitudes of the charges (in Coulombs, C)
• r = Distance between the charges (in meters, m)
• k = Coulomb’s constant (8.9875 \times 10^9 \, \text{N.m}^2/\text{C}^2)

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Key Features of Coulomb’s Law

1. Force is Vectorial:
   • Coulomb’s force is a vector quantity, meaning it has both magnitude and direction.
   • The direction depends on the nature of the charges:
     • Like charges (both positive or both negative): Repel each other.
     • Unlike charges (one positive and one negative): Attract each other.
2. Action-Reaction Pair:
   • The force exerted by charge q1​ on q2​ is equal in magnitude and opposite in direction to the force exerted by q2 on q1​, as per Newton’s third law.
3. Works for Point Charges:
   • Coulomb’s law applies accurately to point charges or spherical charges where the distribution of charge is symmetric.
4. Inverse Square Law:
   • The force diminishes as the square of the distance increases. If the distance is doubled, the force becomes one-fourth.

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Coulomb’s Constant (k):

The value of k depends on the medium between the charges. In a vacuum or air:

\boxed{k = \frac{1}{{4\pi \epsilon_0}} = 8.9875 \times 10^9 \, \text{N.m}^2/\text{C}^2 }

Where ϵ0​ (epsilon naught) is the permittivity of free space:

\boxed{ϵ0= 8.854 \times 10^{-12} \, \text{C}^2/\text{N.m}^2}

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Applications of Coulomb’s Law

1. Electrostatic Interactions:
   • Explains the force between charged particles, which is crucial for understanding atomic and molecular interactions.
2. Electric Field Calculations:
   • Used to derive the electric field due to a point charge.
3. Capacitor Design:
   • Plays a role in determining charge distribution and force in capacitors.
4. Physics of Lightning:
   • Helps in understanding how charged clouds interact with the ground.
5. Principle Behind Sensors:
   • Many sensors and devices, like electroscopes, operate on the principles of Coulomb’s law.

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Limitations of Coulomb’s Law

1. Applicable for Point Charges Only:
   • It is not accurate for extended charges with irregular shapes unless the system can be simplified.
2. Medium Dependence:
   • The force varies with the dielectric constant of the medium, which is not accounted for in the simple form of the law.
3. Relativistic Effects:
   • At very high velocities or in cases involving quantum mechanics, Coulomb’s law becomes less accurate.

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Coulomb’s Law in Vector Form

When working in three-dimensional space, the force between charges can be represented as:

\boxed{\vec{F} = k \frac{{q_1 \cdot q_2}}{{r^2}} \hat{r}}

Where r^ is the unit vector pointing from one charge to the other.

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Comparison with Gravitational Force

Coulomb’s law is mathematically similar to Newton’s law of gravitation. However, there are significant differences:

• Gravitational force is always attractive, while Coulomb’s force can be attractive or repulsive.
• Electrostatic forces are much stronger than gravitational forces.

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Example of Coulomb’s Law

Imagine two charges q1=+2 Cand q2=−3 C, placed 1 meter apart in a vacuum. Using Coulomb’s Law:

\boxed{F = k \frac{{|q_1 \cdot q_2|}}{{r^2}}}

Substituting values:

F = 8.9875 \times 10^9 \cdot \frac{{|2 \cdot (-3)|}}{{1^2}}

F = 5.3925 \times 10^{10} \, \text{N}

The force is attractive since the charges are opposite.

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Conclusion

Coulomb’s law provides a foundation for understanding the behavior of electric charges. It is an essential tool in fields like electronics, physics, and engineering. For Indian students, mastering this concept is crucial for exams like GATE, ESE, and university-level courses.

With its simplicity and universal applicability, Coulomb’s law continues to be a cornerstone of classical electrostatics.

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FAQs on Coulomb’s Law of Electric Force