Q1. Two point charges +3 µC and −3 µC are 20 cm apart. Find the force between them.
F = k q₁q₂/r² = 9×10⁹ × 3×10⁻⁶ × 3×10⁻⁶ / (0.2)²
F = 9×10⁹ × 9×10⁻¹² / 0.04
F = 8.1×10⁻² / 0.04 = 2.02 N (attractive)
Electric Charges and Fields — Class 12
Everything electrostatic starts here. Use the Coulomb calculator to feel the inverse-square force, then practise field and force numericals.
Electric chargeA fundamental property; charge is quantized (q = ne) and conserved. Like charges repel, unlike attract. SI unit: coulomb (C).
Coulomb's lawThe force between two point charges: F = k·q₁·q₂/r², where k = 9×10⁹ N·m²/C². It obeys the inverse-square law.
Electric field (E)The force per unit positive charge, E = F/q = kQ/r². A vector, unit N/C or V/m. Field lines start on + and end on − charges.
Gauss's lawThe total electric flux through a closed surface equals the enclosed charge divided by ε₀: Φ = q/ε₀.
Coulomb's law calculator Interactive
Set two charges and their separation to read the electrostatic force between them.
Force, F = kq₁q₂/r²—N
Halve the distance and the force becomes four times as strong — that is the inverse-square law.
Numericals practice Interactive
Coulomb's law and electric-field problems with steps.
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Solved numericals
Q2. How many electrons make up a charge of −1 C?
q = n e ⇒ n = q/e
n = 1 / (1.6×10⁻¹⁹)
n = 6.25×10¹⁸ electrons
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Coulomb's law | F = k q₁ q₂ / r² | N (k = 9×10⁹) |
| Electric field | E = F/q = k Q / r² | N/C |
| Gauss's law | Φ = q / ε₀ | N·m²/C |
| Field of a point charge | E = k Q / r² | N/C |
| Charge quantization | q = n e | C (e = 1.6×10⁻¹⁹) |
Common mistakes & exam wins
- Coulomb's law is an inverse-SQUARE law — always square the distance.
- Electric field points away from a positive charge and towards a negative charge.
- Charge is quantized (q = ne) and always conserved.
- Gauss's law is easiest for symmetric charge distributions (sphere, line, plane).
Frequently asked questions
What is Coulomb's law?
The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them: F = kq₁q₂/r².
What is an electric field?
The region around a charge where another charge experiences a force; numerically the force per unit positive charge, E = F/q, in N/C.
What is Gauss's law?
The net electric flux through any closed surface equals the total charge enclosed divided by ε₀ (Φ = q/ε₀).
What does it mean that charge is quantized?
Charge exists only in integer multiples of the elementary charge e = 1.6×10⁻¹⁹ C, so q = ne.