Electric Field & Coulomb's Law Calculator

Electric Fields Guide

What do I need to know about Coulomb's Law?

F = kq₁q₂/r², where k = 8.99×10⁹ N·m²/C² (Coulomb's constant), q₁ and q₂ are charges in Coulombs, and r is the distance in metres. Like charges (both positive or both negative) repel; opposite charges attract. The force follows an inverse-square law, just like gravity. Example: two charges of 1 μC separated by 10 cm: F = 8.99×10⁹ × 10⁻⁶ × 10⁻⁶ / 0.01 = 0.899 N.

What should I know about Electric Field Strength?

Electric field strength E = F/q = kq/r², measured in N/C or V/m. It is the force per unit positive charge at that point. The field around a positive charge points outward; around a negative charge it points inward. Field lines never cross. The Earth's atmosphere has an electric field of approximately 100–200 V/m near the surface (negative charge on the ground, positive at high altitude). Near a thundercloud, field strengths can reach 20,000 V/m, triggering lightning.

What should I know about Electric Potential?

Electric potential V = kq/r, measured in volts. It is the work done per unit charge to bring a positive charge from infinity to that point. Potential energy of two charges: U = kq₁q₂/r. Electric potential is a scalar (no direction), while electric field is a vector. The relationship: E = −dV/dx (field is the negative gradient of potential). Equipotential surfaces are perpendicular to field lines.

What's the key thing to understand about Everyday Applications?

Photocopiers (xerography): use electric fields to attract toner particles to charged areas. Inkjet printers: charge droplets and deflect them with electric fields. Electrostatic precipitators: ionise smoke particles so they are attracted to oppositely charged plates — removes 99.9% of particulates from power station flue gas. Defibrillators: use electric current to reset heart rhythm. Capacitors: store electric charge and energy for smoothing power supplies in all electronic devices.

What's the key thing to understand about Electric Field Lines?

Electric field lines are a visual convention for representing the direction and relative strength of an electric field at every point in space, following several fixed rules. Field lines always point away from positive charges and toward negative charges, reflecting the direction a positive test charge would be pushed or pulled. The density of field lines (how closely packed they are) represents field strength — lines drawn closer together indicate a stronger field, which is why field lines are always densest near a charge and spread further apart with distance, matching the inverse-square weakening of the field itself. Field lines never cross one another, because at any given point in space the electric field can only point in one single direction — two crossing lines would imply two different directions at the same point, which is physically impossible. Field lines also always meet a conductor's surface at exactly 90°, since charges rearrange themselves on a conductor until the surface becomes an equipotential, with no component of the field running along it. These rules make field line diagrams a reliable visual shorthand for predicting how a charge will behave at any point in a given field.

What should I know about the Superposition of Electric Fields?

When more than one charge is present, the total electric field at any point in space is simply the vector sum of the individual electric fields each charge would produce on its own — this is the principle of superposition, and it holds because electric fields obey linear physics with no interaction between the individual field contributions themselves. In practice, this means you calculate the field due to each charge separately using E = kq/r² (with its own direction, pointing away from a positive source charge or toward a negative one), and then add all these individual field vectors together, accounting for both magnitude and direction, to find the net field. For two charges of the same sign, their fields partially reinforce and partially cancel depending on position, while for opposite charges (like a dipole), the fields point in similar directions in the region between them, strengthening the combined field there. Superposition is what makes complex charge arrangements — multiple point charges, charged plates, or charged spheres — mathematically tractable: rather than solving one complicated problem, you solve several simple ones and add the results.

What should I know about the Electric Field Between Parallel Plates?

Between two oppositely charged parallel plates separated by distance d with potential difference V across them, the electric field is uniform (same strength and direction everywhere between the plates) and given simply by E = V/d. This is the field configuration inside a capacitor, and it's also how old cathode-ray tube televisions and oscilloscopes deflected electron beams — a uniform field between deflection plates applies a constant force to passing electrons, bending their path by an amount controlled by the applied voltage.

What Do Real Electric Field Strengths Look Like in Nature and Technology?

Electric field strength (measured in volts per metre, V/m) spans many orders of magnitude between everyday and extreme contexts, which helps put an abstract V/m number into physical perspective.

Worked example: using Coulomb's law, the electric field at a distance of 2 metres from a point charge of 5 microcoulombs is E = kQ/r² = (8.99x10^9 x 5x10^-6) / 2² = 44,950/4 ≈ 11,238 V/m. That's comparable in order of magnitude to the field strength measured directly beneath a high-voltage transmission line — a useful sanity check that the calculated value sits in a physically reasonable range rather than being off by several orders of magnitude due to an arithmetic or unit-conversion slip.

How Does Electric Field Strength Relate to Electric Potential (Voltage)?

Electric field and electric potential are closely related but distinct quantities that are easy to conflate. The electric field (in V/m) describes the force per unit charge at a point in space and has direction; electric potential (in volts) describes the energy per unit charge and has no direction, only magnitude. For a uniform field, the relationship is simple: E = V/d, where V is the potential difference between two points and d is the distance between them. This is why increasing the distance between two charged plates at a fixed voltage reduces the field strength between them, and conversely why a very small gap between two points at a modest voltage difference can produce an intense field — exactly the mechanism behind both capacitor design and the risk of electrostatic discharge across a small, close gap even at voltages that would otherwise seem unremarkable.

How Does the Electric Field From a Point Charge Change With Distance?

Electric field strength from a point charge follows an inverse-square law (E = kQ/r²), meaning doubling the distance from the charge reduces the field to one quarter of its original strength, not one half. This is the same mathematical relationship that governs gravity and light intensity with distance, and it's a frequent source of error when people intuitively assume a linear (halving) relationship instead. Worked example: a charge produces a field of 1,000 V/m at a distance of 1 metre. At 2 metres, the field drops to 1,000 / 2² = 250 V/m — a quarter of the original, not half — and at 3 metres it drops further to 1,000 / 3² ≈ 111 V/m, illustrating how quickly field strength falls off with distance even though the charge itself hasn't changed at all.

Worked Example: Field Strength Between Parallel Plates

Two parallel plates are separated by 2cm (0.02m) and connected to a 12V battery. The electric field between parallel plates is uniform and given by E = V/d, where V is the potential difference and d is the plate separation in metres. Substituting the values: E = 12V / 0.02m = 600 V/m (equivalently, 600 N/C). This field strength is uniform everywhere between the plates except near the edges, where fringing effects slightly distort the otherwise straight, parallel field lines. If the plate separation were instead halved to 1cm while keeping the same 12V, the field would double to 1,200 V/m, since field strength is inversely proportional to separation at constant voltage. This relationship is exactly why capacitors with very thin dielectric layers can sustain extremely strong internal fields from comparatively small applied voltages, and why insulation breakdown becomes a real engineering concern as components are miniaturised.