Electricity & MagnetismE = kq/r²

Electric Field Simulator

Place positive and negative point charges and visualize the resulting electric field lines and equipotential contours.

Parameters

q₁ magnitude

μC

q₁ sign

q₂ magnitude

μC

q₂ sign

Equipotentials

Positive charge

Negative charge

Field lines

q₁3.00 μC

q₂-3.00 μC

E at midpoint0 N/C

F (Coulomb)0.0000 N

About Electric Fields

An electric field describes the force per unit charge at every point in space. A positive test charge placed at any location will feel a force in the direction of the local field vector. For a single point charge, the field radiates outward (for positive) or inward (for negative) with magnitude E = kq/r².

ℹElectric field lines always point from positive to negative charges and never cross each other. The density of lines represents the field strength.

Key Variables

Symbol	Name	Unit	Description
k_e	Coulomb Constant	N·m²/C²	8.9875 × 10⁹
q	Charge	C	Source charge magnitude
r	Distance	m	Separation from charge
E	Electric Field	N/C	Force per unit positive charge
F	Coulomb Force	N	Force between two point charges
V	Electric Potential	V	Potential energy per unit charge

Superposition Principle

When multiple charges are present, the total electric field at any point is the vector sum of contributions from each charge. This superposition principle allows us to build complex field configurations from simple point-charge solutions.

Field Line Tracing

Field lines are drawn by starting near a positive charge and stepping in the direction of the local E field at each point. The algorithm terminates when a negative charge is reached, the boundary is hit, or the maximum step count is exceeded.

💡Toggle equipotential lines to see surfaces of constant electric potential — they are always perpendicular to field lines.

Key Formulas

Coulomb's Law

F = k_{e} \frac{q _{1} q _{2}}{r ^{2}}

The force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

Electric Field from a Point Charge

E = k_{e} \frac{q}{r ^{2}} \overset{r}{^}

Superposition

E_{total} = i \sum E_{i} = i \sum k_{e} \frac{q _{i}}{r _{i}^{2}} \overset{r}{^}_{i}

Electric Potential

V = k_{e} \frac{q}{r}

ℹEquipotential surfaces satisfy V = constant. For two charges, these are more complex closed surfaces that bulge toward the weaker charge.

Frequently Asked Questions

Why do field lines start on positive and end on negative charges?

By convention, field lines point in the direction a positive test charge would move. Positive charges exert a repulsive force (lines point away) and negative charges attract (lines point in).

What does field line density represent?

Closer field lines indicate a stronger electric field. The magnitude |E| is proportional to the density of lines per unit area perpendicular to the field direction.

Why are equipotential lines perpendicular to field lines?

Moving along an equipotential surface does no work (dV = 0). Since E = -∇V, the field must point in the direction of maximum potential decrease — always perpendicular to constant-potential surfaces.

What is the electric field at the exact location of a point charge?

Theoretically it diverges to infinity. In practice, real charges have finite size. The simulator caps the field to zero inside a small radius to avoid numerical issues.