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Physics Class 12 - Coulomb's Law
F = kq₁q₂/r²
9.0000e+9 N
Formulas
F = kq₁q₂/r²
Coulomb's Law
k = 9×10⁹ N⋅m²/C²
Coulomb constant
Electrostatics - Class 12 Physics Complete Guide
Electrostatics is the study of electric charges at rest and the phenomena associated with them. This fundamental branch of physics, covered extensively in Class 12 Physics, deals with electric forces, electric fields, electric potential, and capacitance. Understanding electrostatics is essential for grasping how electricity works and forms the foundation for studying current electricity, electromagnetism, and many modern technologies from capacitors in electronics to particle accelerators.
Electric Charge: The Fundamental Concept
Electric charge is a fundamental property of matter that causes it to experience electromagnetic force. There are two types of electric charges: positive (protons) and negative (electrons). Like charges repel each other, while unlike charges attract. The SI unit of charge is the Coulomb (C). The smallest unit of charge is the electron charge (e = 1.602 × 10^-19 C), though in electrostatics calculations we often use microcoulombs (μC) where 1 μC = 10^-6 C.
Coulomb's Law
Coulomb's Law describes the electrostatic force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them:
Where:
- F = Electrostatic force in Newtons
- q₁, q₂ = Electric charges in Coulombs
- r = Distance between charges in meters
- k = Coulomb's constant (9 × 10⁹ N⋅m²/C²)
Electric Field
The electric field is defined as the force per unit charge experienced by a small positive test charge placed at that point. It represents the influence that charged objects create in the space around them:
The direction of the electric field is the direction of the force on a positive test charge. Electric field is a vector quantity, measured in N/C (Newtons per Coulomb) or V/m (Volts per meter).
Electric Potential
Electric potential at a point is the work done in bringing a unit positive charge from infinity to that point. It is a scalar quantity measured in Volts:
Potential difference between two points is the work done in moving a unit charge from one point to the other. Remember: potential due to a positive charge is positive, and due to a negative charge is negative.
Relationship Between E and V
The electric field is the negative gradient of potential. This means E points in the direction of maximum decrease of potential.
Solved Examples
Example 1: Two charges of +2 μC and -3 μC are placed 0.1 m apart. Find the force between them.
Solution:
q₁ = +2 × 10^-6 C, q₂ = -3 × 10^-6 C, r = 0.1 m
F = (9 × 10⁹) × |2 × 10^-6 × (-3) × 10^-6| / (0.1)²
F = (9 × 10⁹) × (6 × 10^-12) / 0.01 = 5.4 N
The force is attractive (negative sign indicates attraction).
Example 2: Calculate the electric field at a point 0.2 m from a charge of +5 μC.
Solution:
Q = +5 × 10^-6 C, r = 0.2 m
E = kQ/r² = (9 × 10⁹) × (5 × 10^-6) / (0.2)²
E = 45 × 10³ / 0.04 = 1.125 × 10⁶ N/C
Key Formulas Summary
| Quantity | Formula | Unit |
|---|---|---|
| Coulomb's Law | F = kq₁q₂/r² | Newton (N) |
| Electric Field | E = kQ/r² | N/C or V/m |
| Electric Potential | V = kQ/r | Volt (V) |
| Coulomb's Constant | k = 1/4πε₀ | 9 × 10⁹ N⋅m²/C² |
Real-World Applications
- Capacitors: Store electrical energy in devices like radios, TVs, and computer memory
- Electrostatic Precipitators: Remove dust and pollutants from industrial chimneys
- Photocopiers: Use electrostatic charges to transfer toner onto paper
- Lightning: Result of electrostatic discharge between charged clouds and ground
- Van de Graaff Generator: Produces high voltages through electrostatic principles
- Electrostatic Painting: Apply even coats of paint to metal objects
Important Principle: The superposition principle states that the total force or field at a point due to multiple charges is the vector sum of individual forces or fields. This allows us to analyze complex charge distributions by considering each charge separately and adding their effects.