Electric Field Calculator Coulomb's Law & Fields
Calculate Coulomb's law, field strength, electric potential, and work done with step-by-step solutions. Perfect for GCSE and A-Level Physics.
Coulomb's law: F = force (N), Q = charge (C), r = distance (m)
Solve for:
Quick charge presets:
Can be negative for negative charges
Can be negative for negative charges
Must be greater than zero
Force between two point charges
Field strength = force per unit charge
Field from a point charge
Field between parallel plates
Potential at distance r from a point charge
Work done moving charge through potential difference
Work done in a uniform electric field
What Are Electric Fields?
An electric field is a region around a charged object where other charges experience a force. Every charged particle creates an electric field that extends outward into the space around it. The field concept, introduced by Michael Faraday, allows us to explain how charges exert forces on each other without touching.
Coulomb's Law
The force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance
Electric field lines visualise the field. They point from positive to negative charges. Closer lines indicate a stronger field. For a single positive charge, lines radiate outward; for a negative charge, they point inward.
Radial Fields (Point Charges)
- • Field lines radiate outward/inward
- • Strength follows E = kQ/r² (inverse square)
- • Gets weaker with distance
- • Field lines are not parallel
Uniform Fields (Parallel Plates)
- • Parallel, equally-spaced field lines
- • Strength is constant: E = V/d
- • Same everywhere between the plates
- • Points from + plate to - plate
Key Electric Field Formulas
Coulomb's Law
The electrostatic force between two point charges. k = 8.99 × 10⁹ N·m²/C².
Same sign = repulsive
Opposite signs = attractive
Double r = quarter the force
Inverse square law
Electric Field Strength
Three forms: definition (F/q), radial field (kQ/r²), and uniform field (V/d).
Key fact: N/C and V/m are the same unit. Electric field strength = force per unit positive charge = potential gradient.
Electric Potential
Potential is energy per unit positive charge. Unlike field strength, it is a scalar (no direction). It can be positive or negative depending on the sign of Q.
Work & Energy
Work done moving a charge through a potential difference (W = qV) or through a uniform field (W = qEd).
1 electronvolt (eV) = work to move one electron through 1 V = 1.602 × 10⁻¹⁹ J
Electric vs Gravitational Fields
Electric and gravitational fields share many mathematical similarities. Comparing them helps deepen understanding of both.
| Property | Electric Field | Gravitational Field |
|---|---|---|
| Force law | F = kQ₁Q₂/r² | F = Gm₁m₂/r² |
| Field strength | E = F/q = kQ/r² | g = F/m = GM/r² |
| Potential | V = kQ/r | V = -GM/r |
| Constant | k ≈ 9 × 10⁹ | G ≈ 6.67 × 10⁻¹¹ |
| Source | Charge (+ or -) | Mass (always +) |
| Force type | Attract or repel | Always attract |
Worked Examples
Practice with these GCSE and A-Level style electric field problems:
Example 1: Force Between Two Charges
Two charges of +3 µC and -5 µC are separated by 0.2 m. Calculate the force between them.
Solution:
Given: Q₁ = 3 × 10⁻⁶ C, Q₂ = -5 × 10⁻⁶ C, r = 0.2 m
F = kQ₁Q₂/r² = (8.99×10⁹)(3×10⁻⁶)(-5×10⁻⁶)/(0.2)²
F = (8.99×10⁹)(-15×10⁻¹²)/(0.04)
F = -3.37 N (attractive, since opposite charges)
Example 2: Uniform Field Between Plates
Two parallel plates are separated by 5 cm with a potential difference of 2000 V. Find the electric field strength.
Solution:
Given: V = 2000 V, d = 5 cm = 0.05 m
E = V/d = 2000/0.05
E = 40,000 V/m = 4 × 10⁴ N/C
Remember: convert cm to m before calculating!
Example 3: Work Done on an Electron
An electron is accelerated through a potential difference of 500 V. Calculate the kinetic energy gained.
Solution:
Given: q = 1.602 × 10⁻¹⁹ C, V = 500 V
W = qV = (1.602 × 10⁻¹⁹)(500)
W = 8.01 × 10⁻¹⁷ J = 500 eV
This is also the kinetic energy gained by the electron.
Example 4: Electric Potential from a Point Charge
Calculate the electric potential at 0.3 m from a +2 µC charge.
Solution:
Given: Q = 2 × 10⁻⁶ C, r = 0.3 m
V = kQ/r = (8.99×10⁹)(2×10⁻⁶)/0.3
V = (1.798×10⁴)/0.3
V = 59,900 V ≈ 6.0 × 10⁴ V
Common Mistakes in Electric Field Problems
Avoid these frequent errors when solving electric field questions in GCSE and A-Level Physics exams:
Forgetting to convert µC and nC to Coulombs
Exam questions often give charges in microcoulombs (µC) or nanocoulombs (nC). You must convert: 1 µC = 10⁻⁶ C, 1 nC = 10⁻⁹ C.
Always check the units of charge. Multiply µC by 10⁻⁶ and nC by 10⁻⁹ before substituting into any formula.
Forgetting to square the distance in Coulomb's law
The formula is F = kQ₁Q₂/r², not F = kQ₁Q₂/r. Missing the square dramatically changes the answer.
Always write out r² explicitly. Calculate r² separately before dividing.
Using E = V/d for radial fields
E = V/d only applies to uniform fields (parallel plates). For point charges, you must use E = kQ/r².
Ask: "Is this a uniform or radial field?" Parallel plates = E = V/d. Point charge = E = kQ/r².
Confusing field strength (vector) with potential (scalar)
Field strength E has a direction (vector). Potential V has no direction (scalar). They have different formulas: E = kQ/r² vs V = kQ/r.
E falls off as 1/r², V falls off as 1/r. E has direction, V does not. Don't mix up the formulas.
Using centimetres instead of metres
All SI formulas require metres. Using cm gives answers that are wrong by factors of 100 or 10,000.
Convert all distances to metres before substituting. Divide cm by 100.
Sign errors in Coulomb's law
Negative force means attraction, positive means repulsion. Students sometimes discard the negative sign or apply it incorrectly.
Keep the sign of Q₁Q₂ throughout the calculation. State whether the force is attractive or repulsive based on the sign.
Frequently Asked Questions
What is Coulomb's law used for?
Coulomb's law calculates the electrostatic force between two point charges: F = kQ₁Q₂/r². It tells you how strong the force is and whether it's attractive (opposite charges) or repulsive (like charges).
What does N/C mean?
N/C stands for newtons per coulomb — the SI unit for electric field strength. It is equivalent to V/m (volts per metre). Both describe the force experienced per unit positive charge.
When do I use E = V/d vs E = kQ/r²?
Use E = V/d for uniform fields between parallel plates. Use E = kQ/r² for the radial field around a point charge. Check whether the question describes plates or a point charge.
What is the difference between E and V?
E (field strength) is a vector — it has direction and magnitude, measured in N/C. V (potential) is a scalar — no direction, measured in V. E ∝ 1/r², V ∝ 1/r for point charges.
Why is electric potential a scalar?
Potential V represents energy per unit charge, and energy is a scalar quantity (no direction). You can add potentials from multiple charges directly. Field strength E is a vector because force has direction.
What is an electron-volt (eV)?
An electron-volt is the energy gained by one electron moving through 1 V of potential difference. 1 eV = 1.602 × 10⁻¹⁹ J. It is used in particle physics because joules are too large.
How strong are electric forces compared to gravity?
Electric forces are vastly stronger. For two protons: the electric repulsion is about 10³⁶ times stronger than their gravitational attraction. This is why gravity only dominates at astronomical scales.
Can electric potential be negative?
Yes! V = kQ/r, so if Q is negative, V is negative. Negative potential means energy is released when a positive test charge moves from infinity to that point.
What is the permittivity of free space?
ε₀ = 8.85 × 10⁻¹² F/m. It relates to how easily electric field lines pass through a vacuum. Coulomb's constant k = 1/(4πε₀). You may see either form in exam formulae sheets.
Is this calculator suitable for GCSE and A-Level?
Yes! It covers GCSE topics (E = V/d, E = F/q, W = qV) and A-Level topics (Coulomb's law, E = kQ/r², V = kQ/r, W = qEd) with step-by-step solutions and learn mode.
Explore More Free Tools
All our tools are 100% free with step-by-step learning