How this instrument works
An electric field is a map of how hard some charge would be pushed or pulled at each point around a source, expressed as force per unit charge rather than force itself. Start from Coulomb's law, F = kQq₀ ⁄ r², and divide out the test charge q₀: what remains, E = kQ ⁄ r², depends only on the source charge Q and the distance r — q₀ cancels out completely. That cancellation is the whole point of the concept: Q sets up something in the surrounding space whether or not a second charge ever arrives to feel it.
Michael Faraday, who had almost no training in the calculus that dominated electrical theory in the 1830s, pictured lines of force radiating outward from every charge and reasoned about their crowding and curvature rather than writing equations. Continental physicists mostly dismissed this as a sketch, not a mechanism, until James Clerk Maxwell spent the 1860s turning Faraday's lines into field equations and arguing that the field itself carries energy and can persist in empty space after its source moves. The unit this sheet reports, newtons per coulomb, is numerically identical to volts per metre — the reading a probe would register at that spot regardless of what, if anything, sits there.
The inverse-square shape holds only outside a source that is genuinely point-like, or spherically symmetric with r measured from its centre; a charged disc, wire, or oddly shaped conductor produces a different field entirely, and Gauss's law is what tells you when the point-charge shortcut is safe. Real setups rarely hold just one source — bring a second charge nearby and the two fields add vector by vector, which is why this sheet reports one contribution at a time rather than a total. Push r toward zero and E climbs without limit, a reminder that no physical charge is truly a dimensionless point; some finite sphere sits underneath, and the formula only takes over outside it.
- Enter your source charge into Point charge, choosing nC, µC, mC or C from the unit menu — most static and bench charges are nanocoulombs or smaller.
- Set Distance from the charge to how far out you want the field evaluated, measured from the charge's centre, in mm, cm or m.
- Read Electric field in newtons per coulomb, numerically the same as volts per metre — the push per coulomb that anything at that spot would feel.
- To find the actual force on some other charge sitting there, multiply this reading by that charge's own value in coulombs; this sheet stops at the field.
- A negative Point charge simply reverses the sign of the reading, meaning the field points inward instead of outward; its size is unaffected.
Worked example — a 5 nC charge, 10 cm away
Set Point charge to 5 nC and Distance from the charge to 10 cm — a charge in the range a small object picks up rubbing against wool, read a hand's width away. E = kq ⁄ r² = (8.9875517874 × 10⁹)(5 × 10⁻⁹) ⁄ (0.1)² = 4,493.78 N/C. That is the push, per coulomb, that some other charge would feel if it were placed at that exact spot — not a force on any particular object, since none has been specified yet.
Push Distance from the charge out to 20 cm without touching the charge itself and the reading falls to 1,123.44 N/C — not half of 4,493.78 but a quarter, because doubling r squares the denominator. That quartering is the inverse-square law restated as a lived number, the same curve an ESD engineer reads when checking whether a charged component's field will cross dry air's roughly 3 × 10⁶ V/m breakdown threshold at some clearance, just rescaled to microcoulombs and millimetres.
Questions
What's the difference between electric field and electric force?
The field, E, is what the source charge alone creates at a point in space — newtons per coulomb, independent of any second charge. Force, F = qE, is what a specific charge actually feels once it sits there. A 5 nC charge at 10 cm sets up 4,493.78 N/C regardless of whether anything occupies that spot; only once you place, say, a 2 µC charge there does a force appear, found by multiplying the field by that charge: about 8.99 × 10⁻³ N.
Why does the formula not need to know about a second charge?
Because the field is built by dividing Coulomb's force by the test charge that would feel it: E = F/q₀ = kQq₀/(r²q₀), and q₀ cancels completely. What survives depends only on the source charge Q and the distance r, which is exactly why physicists treat the field as belonging to Q itself rather than to whatever test charge happens to measure it — the field exists whether or not one is ever brought in.
Can the electric field reading come out negative?
Yes, and the sign gives direction rather than signalling an error. This sheet computes E = kq/r² without discarding the sign of q, so a negative source charge returns a negative E, meaning the field points inward, toward the charge, instead of outward. Flip Point charge from +5 nC to −5 nC and the reading flips from 4,493.78 N/C to −4,493.78 N/C; the size a nearby charge would feel is identical either way.
Why does doubling the distance quarter the field instead of halving it?
Because the field weakens with the square of distance, not distance itself. Doubling r from 10 cm to 20 cm divides E by 2² = 4, taking the 5 nC example from 4,493.78 N/C down to 1,123.44 N/C — a quarter, not a half. Geometrically, the same field lines from q spread over a sphere whose surface area grows as r², so the density crossing any patch of it falls at that same rate.
Does this formula still work for a charged sphere, not just a true point?
Outside the sphere, yes. Gauss's law guarantees that any spherically symmetric charge behaves, from outside its own surface, exactly as if all of it sat at the centre — set r from that centre and E = kq/r² applies unchanged. Step inside a uniformly charged insulating sphere and the field instead grows linearly with r; inside a hollow conductor it drops to zero. Neither interior case is what this sheet computes.
What does a zero reading mean?
Either input is zero. Set Point charge to 0 and E reads 0 at any distance, since an absent source creates no field. Set Distance from the charge to 0 and the formula instead grows without bound rather than settling at zero — a true point charge has an undefined, infinite field at its own location, which is why this sheet requires r greater than zero and treats zero distance as an error, not an answer.