Electric Field Formula
Reference for the electric field formula E = kQ over r squared.
Calculate field strength from a point charge, direction conventions, and worked examples.
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The Formula
E = k × |q| / r²
The electric field describes the force that would be exerted on a positive test charge at any point in space. It points away from positive charges and toward negative charges.
Variables
| Symbol | Meaning |
|---|---|
| E | Electric field strength (N/C or V/m) |
| k | Coulomb's constant (8.99 × 10⁹ N⋅m²/C²) |
| q | Source charge creating the field (Coulombs) |
| r | Distance from the charge (meters) |
Example 1
Find the electric field 0.3 m from a +5 μC charge
E = 8.99 × 10⁹ × 5 × 10⁻⁶ / (0.3)²
E = 44,950 / 0.09
E ≈ 499,444 N/C ≈ 5.0 × 10⁵ N/C
Example 2
What force does a +2 μC charge feel in a field of 1000 N/C?
F = q × E = 2 × 10⁻⁶ × 1000
F = 0.002 N = 2 mN
When to Use It
Use the electric field formula when:
- Mapping the electric field around charged objects
- Calculating the force on a charge placed in an external field
- Designing capacitors and electronic components
- Understanding how electric fields store energy
Key Notes
- The inverse-square relationship means doubling the distance reduces the field by a factor of 4, not 2 — field strength falls off rapidly with distance
- The formula applies to a point charge in a vacuum or air — inside a dielectric material, the field is weakened by the relative permittivity: E = kq / (εᵣ r²)
- Field direction follows the source charge: positive charges create fields pointing outward; negative charges create fields pointing inward — the test charge is always assumed positive
- Superposition principle: fields from multiple charges add as vectors at any given point; the net field is found by vector-summing each charge's individual contribution
Key Notes
- Definition: E = F / q: The electric field at a point is the electrostatic force per unit positive test charge placed there. Unit: N/C = V/m. The field exists whether or not a test charge is present — it is a property of the space surrounding source charges.
- Point charge: E = kq / r²: k = 8.99×10⁹ N·m²/C². Field points away from a positive source charge and toward a negative one. The magnitude falls off as 1/r² (inverse square law), just like gravity.
- Uniform field: E = ΔV / d: Between two parallel plates with potential difference ΔV separated by distance d, the field is uniform (constant magnitude and direction). This is how capacitors work — the field stores energy that accelerates charges.
- Superposition principle: The total electric field from multiple charges is the vector sum of each individual contribution: E_total = Σ E_i. Fields add as vectors — directions matter. For symmetric charge distributions, many contributions cancel, simplifying calculations.
- Applications: Electric field analysis governs capacitor design (field between plates), electron beam focusing in CRTs and electron microscopes, electrostatic precipitator operation (removing particles from air), photocopier and laser printer drum charging, and the behavior of biological membrane potentials at ion channel openings.