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By the end of these notes, you should be able to:
A point charge is an idealised (simplified) model of a charged object where all the electric charge is imagined to be concentrated at a single point. In reality, objects have size, but when we are far enough away from them, we can treat them as if all their charge sits at one point. This makes calculations much simpler.
Before using the formula, let's quickly recall what electric field strength means.
Electric field strength (E) is defined as the force experienced per unit of positive charge at a given point in an electric field. In simpler terms: if you place a tiny positive charge at a point in a field, E tells you how much force each coulomb of that charge would feel.
E=qF
When we want to find the electric field strength at a certain distance from a point charge, we use the following equation:
E=4πε0r2Q
Let's look at each part carefully:
| Symbol | What it means | Unit |
|---|---|---|
| E | Electric field strength at the point | N C⁻¹ or V m⁻¹ |
| Q | The charge producing the electric field (the source charge) | Coulombs (C) |
| ε0 | Permittivity of free space — a fixed constant of nature | F m⁻¹ |
| r | The distance from the centre of the point charge to the point where you want to find E | metres (m) |
| 4πε0 | A combination of constants that appears in all electric field equations | — |
The value of the permittivity of free space is:
ε0=8.85×10−12 F m−1This constant tells us how well a vacuum (empty space) allows an electric field to pass through it.
You will sometimes see the formula written using the shorthand constant k, where:
k=4πε01≈8.99×109 N m2 C−2So the formula can also be written as:
E=r2kQ
Both versions mean exactly the same thing. In A-Level Physics, you are expected to use the full version with 4πε0.
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