Describe simple electric field patterns, including the direction of the field: (a) around a point charge (b) around a charged conducting sphere (c) between two oppositely charged parallel conducting plates (end effects will not be examined)

4.2.1 Electric Charge

(a) Around a Point Charge ⚡️

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:

  • Outward (radially away) if q > 0 (positive charge).
  • Inward (radially toward) if q < 0 (negative charge).

ChargeField DirectionField Strength
\$+q\$Outward (↗️)\$E = \dfrac{kq}{r^2}\$
\$-q\$Inward (↘️)\$E = \dfrac{k|q|}{r^2}\$

(b) Around a Charged Conducting Sphere 🟢

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\$.

  • Field lines start (or end) on the sphere’s surface and are perpendicular to it.
  • Field strength decreases with the square of the distance from the centre.

RegionField DirectionField Strength
Inside (r < R)None (0)\$0\$
Outside (r > R)Outward if Q > 0, Inward if Q < 0\$E = \dfrac{kQ}{r^2}\$

(c) Between Two Oppositely Charged Parallel Conducting Plates 🟠

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.

  • Direction: from + plate to – plate (↔️).
  • Magnitude is constant between the plates.
  • No field lines start or end on the plates themselves; they terminate on the opposite plate.

LocationField DirectionField Strength
Between the platesFrom + to – (↔️)\$E = \dfrac{\sigma}{\varepsilon_0}\$
Outside the platesNone (≈0)\$0\$