The Electric Field & Field Lines
Charges fill space with a field that pushes on other charges.
Lesson at a glanceShow the key points
- A charge creates a field that exerts force on other charges; changes propagate at speed c.
- E⃗ = F⃗/q (29.3) with a small test charge; point charge E = Q/4πε₀r² (29.4).
- Fields add as vectors; continuous charges by integration. Ring on its axis: E = Qx/4πε₀(a² + x²)^(3/2).
- Field lines: tangent gives direction, density gives strength; from + to −; no physical existence.
Charges don’t reach across space to tug each other directly. Each fills the space around it with an electric field, and the field pushes on other charges.
The electric field
A charge produces an electric field around it, which exerts forces on other charges placed there. The field exists whether or not anything is there to feel it, and it takes time to change: move a charge and the field a distance r away changes only after r/c.
Field of a point charge
+8.0 µC and −8.0 µC are 6.0 cm apart. Find the field at a point on the perpendicular bisector 4.0 cm from their midpoint.
Continuous charge: a ring
For spread-out charge, add the fields of small pieces dQ by integration. For a ring of radius a with charge Q, at a point on its axis a distance x from the centre, the sideways components cancel by symmetry and the axial parts add:
Lines of force
Field lines are drawn so that the tangent at each point gives the field direction there. From a positive point charge they spread straight outward; into a negative one they converge. Drawn evenly from each charge, the number of lines crossing a small area at right angles is proportional to the field strength: crowded lines, strong field.
- 1A charge creates a field; the field exerts force F⃗ = qE⃗ on other charges.
- 2E⃗ = F⃗/q with a small test charge; point charge E = Q/4πε₀r².
- 3Fields add as vectors; continuous charge needs integration (ring: Qx/4πε₀(a² + x²)^(3/2)).
- 4Field lines: tangent = direction, density = strength; from + to −.
Check yourself
Keep exploring
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