Think of a tiny charged balloon floating in space. The electric field lines radiate from the balloon if it is positively charged, or converge onto it if it is negatively charged. The field strength decreases with distance, following the inverse‑square law:
\$E = \dfrac{k\,q}{r^2}\$,
where k is Coulomb’s constant, q is the charge, and r is the distance from the charge. The direction of the field is always:
| Charge | Field Direction | Field Strength |
|---|---|---|
| \$+q\$ | Outward (↗️) | \$E = \dfrac{kq}{r^2}\$ |
| \$-q\$ | Inward (↘️) | \$E = \dfrac{k|q|}{r^2}\$ |
Imagine a smooth metal ball that has been given a net charge. Inside the metal, the electric field is zero because free electrons rearrange themselves to cancel any internal field. Outside, the field behaves exactly like that of a point charge located at the centre of the sphere:
\$E_{\text{outside}} = \dfrac{k\,Q}{r^2}\$,
where Q is the total charge on the sphere and r is the distance from the centre (with r > R, R being the sphere’s radius). Inside the sphere (r < R), the field is zero:
\$E_{\text{inside}} = 0\$.
| Region | Field Direction | Field Strength |
|---|---|---|
| Inside (r < R) | None (0) | \$0\$ |
| Outside (r > R) | Outward if Q > 0, Inward if Q < 0 | \$E = \dfrac{kQ}{r^2}\$ |
Picture two flat, large plates facing each other, one positively charged and the other negatively charged. The electric field between them is uniform (the same everywhere) and points from the positive plate to the negative plate. End effects (edge distortions) are ignored for this simple model.
\$E = \dfrac{\sigma}{\varepsilon_0}\$,
where σ is the surface charge density on the plates and ε₀ is the permittivity of free space. The field outside the plates is essentially zero.
| Location | Field Direction | Field Strength |
|---|---|---|
| Between the plates | From + to – (↔️) | \$E = \dfrac{\sigma}{\varepsilon_0}\$ |
| Outside the plates | None (≈0) | \$0\$ |