Electrostatics – Stage 1
Chapter 1: Electric Charges & Fields – Page 3
1. Why Electric Field Is Introduced
Force depends on the value of the test charge, which makes analysis inconvenient. To avoid this, physicists introduced a new concept:
Electric Field – a property of space around a charge.
Electric field exists even if no test charge is placed.
2. Definition of Electric Field
Electric field at a point is defined as the electrostatic force experienced by a unit positive test charge placed at that point.
𝐄 = 𝐅 / q₀
where:
- 𝐄 → Electric field
- 𝐅 → Force on test charge
- q₀ → Test charge (→ 0)
3. Important Conditions (JEE FAVORITE)
- Test charge must be very small
- Test charge must be positive
- Test charge must not disturb original field
JEE Trap: Electric field does NOT depend on the test charge.
4. SI Unit & Dimensions
- SI unit: Newton per Coulomb (N/C)
- Alternate unit: Volt per meter (V/m)
Dimensions:
[M L T⁻³ A⁻¹]
5. Electric Field Due to a Point Charge
For a point charge q at distance r:
𝐄 = (1 / 4πε₀) · (q / r²)
Direction:
- Away from positive charge
- Towards negative charge
6. Vector Form (ADVANCED LEVEL)
𝐄⃗ = (1 / 4πε₀) · (q / r²) · r̂
r̂ is the unit vector from charge to field point.
7. Nature of Electric Field
- Vector quantity
- Obeys superposition principle
- Exists independent of test charge
8. Force–Field Relationship
Once electric field is known, force on any charge q is:
𝐅 = q𝐄
This formula is heavily used in JEE numerical problems.
9. Electric Field vs Force (Comparison)
| Electric Field | Force |
|---|---|
| Independent of test charge | Depends on test charge |
| Property of space | Interaction between charges |
| Vector field | Vector force |
Stage 1 – Page 3 Takeaway
- Electric field removes dependency on test charge
- Defined as force per unit positive charge
- Direction follows force on positive charge
- Foundation for field lines, flux & Gauss law
Next → Stage 1, Page 4: Electric Field due to Multiple Charges (Superposition of Fields)
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