Electrostatics – Stage 1
Chapter 1: Electric Charges & Fields – Page 4
1. Concept Introduction
When more than one charge exists, each creates its own electric field. The net electric field at any point is the vector sum of all individual fields. This is called the Principle of Superposition of Electric Fields.
JEE Key Idea: You can treat each charge separately, find its field, and then add all using vector algebra.
2. Formula for Net Electric Field
If charges q₁, q₂, q₃ … are present, and we want field at point P:
𝐄⃗ = 𝐄⃗₁ + 𝐄⃗₂ + 𝐄⃗₃ + …
where each field is:
𝐄⃗ᵢ = (1 / 4πε₀) · (qᵢ / rᵢ²) · r̂ᵢ
3. Step-by-Step Method (IIT Style)
- Mark all charge positions.
- Draw field directions due to each charge.
- Write field magnitudes using Coulomb’s Law.
- Resolve each field into x and y components.
- Add components: 𝐄ₓ = ΣEᵢcosθᵢ, 𝐄ᵧ = ΣEᵢsinθᵢ.
- Find resultant: E = √(𝐄ₓ² + 𝐄ᵧ²).
- Direction: θ = tan⁻¹(𝐄ᵧ / 𝐄ₓ).
4. Special Case: Two Equal Like Charges
Two equal charges q separated by distance 2a, field at mid-point P:
- Fields due to both are equal in magnitude.
- Directions are opposite → cancel each other.
Result: Net field = 0 at midpoint for equal like charges.
5. Special Case: Equal & Opposite Charges
For +q and –q separated by 2a, field at midpoint (equatorial point):
E = (1 / 4πε₀) · (2q / (r² – a²))
Direction → from +q to –q.
6. Example (Numerical Practice)
Two charges +2 μC and +8 μC placed 10 cm apart. Find net field at mid-point.
Solution:
E₁ = (9×10⁹ × 2×10⁻⁶) / (0.05)² = 7.2×10⁶ N/C
E₂ = (9×10⁹ × 8×10⁻⁶) / (0.05)² = 28.8×10⁶ N/C
Net E = E₂ – E₁ = 21.6×10⁶ N/C
Direction → from smaller to larger charge.
Exam Note: Always check direction before final subtraction or addition.
7. Superposition for Electric Fields vs Forces
| Forces | Fields |
|---|---|
| Depends on magnitude of test charge | Independent of test charge |
| 𝐅⃗ = 𝐅₁ + 𝐅₂ + 𝐅₃ | 𝐄⃗ = 𝐄₁ + 𝐄₂ + 𝐄₃ |
| Measured in Newton (N) | Measured in N/C or V/m |
Stage 1 – Page 4 Takeaway
- Electric field follows vector addition.
- Net field = sum of individual fields.
- Use geometry or components for accuracy.
- Symmetry often simplifies calculation.
Next → Stage 1, Page 5: Electric Field Lines – Concept, Rules & Applications
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