At the midpoint between a +5 nC and −5 nC charge separated by 2 m, what is the direction of the electric field?

The correct answer is: Toward the negative charge. Each charge contributes a field at the midpoint. Add them as vectors — they point in the same direction here.

Two equal positive charges: where is the electric field zero?

The correct answer is: At the midpoint between them. By symmetry, the fields cancel at the midpoint. Set q₁=q₂=+5 and observe.

Calculate the force between +5 nC and −5 nC charges separated by 2 m.

The correct answer is: 5.6 × 10⁻⁸ N. F = kq₁q₂/r². Use k = 8.99×10⁹.

Two +3 nC charges and one −6 nC charge form a triangle. Describe the field at the center.

The correct answer is: Points toward the −6 nC charge. You can work it out this way: use superposition. Enable the third charge and set q₁=q₂=+3, q₃=−6 in a triangular configuration.

Why are equipotential surfaces always perpendicular to field lines? Give a physical argument.

The correct answer is: Because no work is done along an equipotential, requiring E⊥displacement. Moving along an equipotential does no work (ΔV=0). Work = qE·d = 0 requires E⊥d.

Pro 🔒~20 min

Electric Field Lines

Visualize fields from point charges in 3D

How it works

Electric field lines show the direction a positive test charge would move. They originate from positive charges, terminate on negative charges, and never cross. The density of field lines represents field strength. When multiple charges are present, the total field at any point is the vector sum of individual fields (superposition principle). Equipotential surfaces are perpendicular to field lines — no work is done moving a charge along an equipotential.

Can you feel the electric force from your phone charger? It's there — you just can't sense it.

Electric fields surround every charged object. The field from your phone charger is real but far too weak for human perception — you'd need billions of times more charge to feel a tingle.

What you'll learn

Field Line Rules. Electric field lines start on positive charges and end on negative charges. They never cross — if they did, a test charge at the crossing point would have two directions to go, which is physically impossible. The density of lines represents field strength.
Coulomb's Law. The electric force between two point charges follows an inverse-square law, just like gravity. Double the distance and the force drops to one-quarter. Double either charge and the force doubles.
Superposition Principle. When multiple charges are present, the total electric field at any point is the vector sum of the individual fields. This means you calculate each charge's contribution independently, then add them as vectors — direction matters!
Equipotential Surfaces. An equipotential surface connects all points at the same electric potential. No work is done moving a charge along an equipotential. These surfaces are always perpendicular to field lines — this is a powerful geometric tool for visualizing fields.
Dipole Fields. A pair of equal and opposite charges (a dipole) creates a characteristic field pattern: lines arc from the positive charge to the negative charge. Far from the dipole, the field falls off as 1/r³ — faster than a single charge. Water molecules are permanent dipoles, which is why water is such a good solvent.

Step-by-step

Adjust the charges of two objects and their separation.
Field lines draw in 3D — use your mouse to orbit and see the full structure.
Try +/+ (repulsion), +/- (attraction), and equal charges.
Pro users can add a third charge and toggle equipotential surfaces.

Key formulas

$\vec{E} = k_e \frac{q}{r^2}\hat{r}$ Electric field from a point charge
$k_e = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$ Coulomb's constant
$\vec{E}_{total} = \sum_i \vec{E}_i$ Superposition principle
$F = k_e \frac{|q_1 q_2|}{r^2}$ Coulomb's law (force between charges)
$V = k_e \frac{q}{r}$ Electric potential from a point charge
$\vec{E} = -\nabla V$ Field is negative gradient of potential

Frequently asked questions

At the midpoint between a +5 nC and −5 nC charge separated by 2 m, what is the direction of the electric field?: The correct answer is: Toward the negative charge. Each charge contributes a field at the midpoint. Add them as vectors — they point in the same direction here.
Two equal positive charges: where is the electric field zero?: The correct answer is: At the midpoint between them. By symmetry, the fields cancel at the midpoint. Set q₁=q₂=+5 and observe.
Calculate the force between +5 nC and −5 nC charges separated by 2 m.: The correct answer is: 5.6 × 10⁻⁸ N. F = kq₁q₂/r². Use k = 8.99×10⁹.
Two +3 nC charges and one −6 nC charge form a triangle. Describe the field at the center.: The correct answer is: Points toward the −6 nC charge. You can work it out this way: use superposition. Enable the third charge and set q₁=q₂=+3, q₃=−6 in a triangular configuration.
Why are equipotential surfaces always perpendicular to field lines? Give a physical argument.: The correct answer is: Because no work is done along an equipotential, requiring E⊥displacement. Moving along an equipotential does no work (ΔV=0). Work = qE·d = 0 requires E⊥d.