Electric field lines — rules, patterns for point charges, dipoles, plates

Question

What are the rules for drawing electric field lines? Describe the field line patterns for point charges, dipoles, and parallel plates.

Solution — Step by Step

Field lines start from positive charges and end on negative charges (or extend to infinity)
The tangent at any point gives the direction of the electric field at that point
Lines are closer together where the field is stronger, farther apart where weaker
Field lines never cross each other (the field has a unique direction at every point)
The number of lines originating from a charge is proportional to the magnitude of the charge
Field lines are perpendicular to the surface of a conductor (in equilibrium)

Single positive charge: Lines radiate outward in all directions, like spokes of a wheel. Uniform spacing at equal distances from the charge.

Single negative charge: Lines converge inward from all directions toward the charge.

Two equal positive charges: Lines repel each other. There is a neutral point (zero field) midway between them. No lines connect the two charges.

Positive + negative (equal): Lines go from the positive to the negative charge, forming smooth curves. This is the dipole pattern — field lines leave the positive charge and enter the negative charge.

Electric dipole: Field lines form closed loops from + to - outside the dipole. Between the charges, the field is strong and roughly uniform along the axis.

Parallel plates (capacitor): Between the plates, field lines are straight, parallel, and equally spaced — indicating a uniform electric field. At the edges, lines curve outward (fringing effect). The field between plates is $E = \sigma/\varepsilon_0 = V/d$ .

Conducting sphere: Outside, the pattern is identical to a point charge at the centre. Inside, there are no field lines ( $E = 0$ inside a conductor).

graph TD
    A[Electric Field Lines] --> B{Charge configuration?}
    B -->|Single +ve| C["Radiate outward"]
    B -->|Single -ve| D["Converge inward"]
    B -->|Dipole: +q and -q| E["+ to - through curves"]
    B -->|Parallel plates| F["Straight, parallel, uniform"]
    B -->|Conductor surface| G["Perpendicular to surface"]

Why This Works

Field lines are a visual tool invented by Faraday to represent the electric field. While the field is a continuous vector function defined at every point in space, field lines give us an intuitive picture.

Key quantitative connection: the density of field lines (number per unit area perpendicular to the lines) is proportional to the field magnitude $E$ . This is why the lines are crowded near charges (strong field) and spread out far away (weak field).

For exams, the most important applications of field lines are:

Identifying where the field is zero (neutral points — between like charges)
Understanding why $E = 0$ inside a conductor
Recognising the uniform field between capacitor plates

Alternative Method

For competitive exams, instead of drawing field lines, we can calculate the field using Coulomb’s law or Gauss’s law:

Gauss’s law: $\oint \vec{E} \cdot d\vec{A} = \frac{q_{enc}}{\varepsilon_0}$

This is faster for symmetric charge distributions (sphere, infinite line, infinite plane). The flux through a closed surface equals the enclosed charge divided by $\varepsilon_0$ .

Common Mistake

Students draw field lines crossing each other, especially near two positive charges. Field lines NEVER cross. At the neutral point between two equal positive charges, the field is zero — there are simply no field lines passing through that point. If two lines crossed, it would mean the field has two directions at that point, which is physically impossible.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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