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Electric Field and Field Lines Explained
Every electric charge fills the space around it with an electric field. The field at a point is the force a small positive test charge would feel there, divided by that charge: E = F/q₀, measured in newtons per coulomb (N/C).
Coulomb's law and the field of a point charge
A point charge q produces a field of size E = k|q|/r² at distance r, where k = 8.99 × 10⁹ N m²/C². It points away from a positive charge and towards a negative one. Double the distance and the field drops to a quarter: it is an inverse-square law.
Superposition
With several charges, each one contributes its own field, and the total is the vector sum of all of them. This simple rule lets you work out the field of any arrangement, from a dipole to a charged plate.
Field lines
- They start on positive charges and end on negative charges.
- Their direction at any point is the direction of the field there.
- They crowd together where the field is strong.
- They never cross, because the field has only one direction at each point.
Field lines are a way of drawing the field; they are not physical objects. The field exists everywhere, including between the lines.
Dipoles and null points
An electric dipole is a pair of equal and opposite charges. Its field lines leave the positive charge and curve round into the negative one. Between two equal positive charges there is a null point, exactly midway, where their fields cancel and E = 0.
Potential and equipotentials
The electric potential V = kq/r (in volts) adds up as ordinary numbers, not vectors. Lines of equal potential, called equipotentials, always cross field lines at right angles, because moving along an equipotential takes no work.
Worked example
A +2 μC charge sits 0.5 m from a point. E = kq/r² = (8.99 × 10⁹ × 2 × 10⁻⁶) / 0.5² ≈ 7.2 × 10⁴ N/C, pointing away from the charge.
Frequently asked questions
What is an electric field?
It is the force per unit charge that a small positive test charge would feel at a point: E = F/q₀. It is measured in N/C.
Why do electric field lines never cross?
At every point the field has a single direction. If two lines crossed, the field would have two directions at the crossing point, which is impossible.
What is a null point?
A point where the electric fields from different charges cancel exactly, so the total field is zero. For two equal positive charges it lies midway between them.
Why are equipotentials perpendicular to field lines?
No work is done moving a charge along an equipotential, so the field can have no component along it. The field must point straight across, at right angles.