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Electricity · Physics

The field lets you predict forces anywhere in space.

An electric field assigns a vector to each point in space: the force per unit positive charge a test charge would feel there. This shifts the focus from “pairs of charges” to a reusable model of space itself.

This topic

Electric Field

Define E, compute it for point charges, combine fields by superposition, and interpret field vectors physically.

Definition
What an electric field is
The electric field at a point is defined as the force per unit positive test charge placed at that point. It is a property of space created by source charges.
  • E = F/q (definition with a test charge)
  • Field exists even if no test charge is present
  • Units: N/C (also V/m later)
  • Direction: direction of force on a positive test charge
Start nano-lesson Field is a model of space.
Source
Field due to a point charge
A point charge creates a radial field. The magnitude decreases with distance, and the direction depends on the sign of the source charge.
  • Magnitude scales as 1/r²
  • Direction: away from +, toward −
  • Radial symmetry and what it implies
  • Using geometry to build components
Start nano-lesson Sign sets direction; distance sets magnitude.
Method
Superposition of electric fields
The net electric field is the vector sum of the fields from each source charge. This is usually easier than summing forces on a specific test charge.
  • Add E-vectors at the same point in space
  • Component addition for non-collinear fields
  • Symmetry shortcuts for balanced configurations
  • Common mistake: adding magnitudes only
Start nano-lesson Compute the field first, then apply it to charges.
Interpretation
Physical meaning of field vectors
Field vectors represent a local rule for force: at each point, a positive test charge would accelerate in the direction of E. Interpreting E correctly prevents sign mistakes later.
  • Force on a charge: F = qE (preview)
  • Negative charges accelerate opposite E
  • Field is continuous; sources are discrete
  • How diagrams encode direction and relative strength
Start nano-lesson Field tells you what force would happen there.
Practice
Practice & Exercises
Practice computing fields at points, adding vectors by superposition, and translating E into force and motion direction for different charge signs.