Electric field and field lines

A charge changes the space around it, even before another charge arrives. This effect is its electric field.

E = F / q₀: the force on a small positive test charge q₀, per unit charge. Unit: N/C. E is a vector.

For a point charge q: E = kq / r². It points away from a positive charge and towards a negative one.

Example: 2 µC, at 30 cm: E = 9 × 10⁹ × 2 × 10⁻⁶ / (0.3)² = 2 × 10⁵ N/C, pointing away.

Once you know E, the force on any charge q placed there is F = qE. A negative charge is pushed opposite to E. An electron in a field of 1000 N/C feels 1.6 × 10⁻¹⁶ N against the field.

Fields from several charges add as vectors (superposition), just like forces.

Field lines are a picture of the field:

• They start on positive charges and end on negative charges (or go off to infinity).
• They are continuous curves with no breaks.
• Two lines never cross: at a crossing, the field would have two directions at one point, which is impossible.
• Where lines are crowded, the field is strong; where they spread out, it is weak.
• They do not form closed loops.

The tangent to a field line at any point gives the direction of E there.