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Electricity · Physics

Field lines help you see direction. Flux helps you measure it.

Field lines are a visualization tool: they show the direction a positive test charge would accelerate. Electric flux is a scalar that measures how much field “passes through” a surface.

This topic

Electric Field Lines and Flux

Learn the rules for drawing field lines and the meaning of flux through flat and curved surfaces.

Visualization
Field lines: what they represent
Electric field lines are a visual representation of the vector field. They do not “exist” physically as strings; they are a drawing rule that encodes direction and relative strength.
  • Line tangent gives the direction of E
  • Lines begin on + charges and end on − charges (or infinity)
  • Lines never cross (field has a unique direction at a point)
  • Field lines are denser where the field is stronger
Start nano-lesson Lines show direction; density hints at magnitude.
Rules
Field line density and field strength
The number of lines you draw is arbitrary, but the relative density should reflect the relative magnitude of the field. Symmetry and charge sign control the pattern.
  • More line density → larger |E|
  • Near a point charge, lines are radial
  • For equal and opposite charges, dipole patterns appear
  • For conductors (electrostatic equilibrium), lines meet the surface perpendicular
Start nano-lesson Keep patterns consistent with symmetry.
Definition
Electric flux
Electric flux measures the field passing through a surface. It depends on the field, the surface area, and the surface’s orientation relative to the field.
  • Flux is a scalar (can be positive, negative, or zero)
  • For uniform field and flat surface: Φ = EA cos(θ)
  • θ is the angle between E and the surface normal
  • Units: N·m²/C
Start nano-lesson Flux uses the surface normal, not the surface itself.
Surfaces
Flux through flat and curved surfaces
For a non-uniform field or a curved surface, you add up contributions from small surface patches. The idea is the same: field component normal to the surface times area.
  • Break the surface into small patches dA
  • Only the normal component of E contributes
  • Closed surfaces: outward normal by convention
  • Sets up Gauss’s law (next topic)
Start nano-lesson Think “sum of E·dA.”
Practice
Practice & Exercises
Practice interpreting field line diagrams and computing flux for simple geometries and orientations.
  • Read direction and relative strength from field lines
  • Decide the sign of flux using the chosen normal
  • Compute flux for uniform fields through tilted planes
  • Concept checks: when is flux zero?
  • Exam-style flux problems (intro)
Open practice sets Draw the surface normal first.