Field lines, vector plots, and the superposition principle
The electric field E describes the force per unit charge at every point in space. A positive charge creates a field that points radially outward; a negative charge pulls the field inward. Multiple charges superpose: the total field is the vector sum of individual contributions. This is Coulomb's law in its field form.
Field lines emanate from positive charges and terminate at negative charges. Their density indicates field strength. Place charges and watch the field pattern emerge from superposition.
Field lines emanate from positive charges and terminate at negative charges. Toggle the placing sign and click to add charges.
Key insight: Field lines never cross. At any point, the field has a unique direction. The density of lines encodes the inverse-square law: twice the distance means one-quarter the field strength.
A vector plot shows the field as arrows at grid points. Each arrow's length and color encode the field magnitude. Add charges to see superposition in action.
Click to add a positive charge. Click an existing charge to remove it. Arrow length and brightness indicate field strength.
Key insight: Superposition is linear: the field from multiple charges is the vector sum of individual fields. This makes electrostatics fundamentally tractable.
An electric dipole is a pair of equal and opposite charges. Far from the dipole, the field falls off as 1/r³ and depends on the dipole moment p = qd. Adjust the separation to see the transition from two distinct charges to a unified dipole pattern.
Adjust the charge separation to see how the dipole field changes. The background heatmap shows field magnitude. At large distances the field falls off as 1/r³ rather than 1/r².
Key insight: Most neutral objects (molecules, antennas) have dipole moments. The 1/r³ far-field pattern is universal for dipoles and dominates at large distances.