All Labs

Electrostatics & Equipotential Mapping Lab

Place positive and negative point charges on a 2D canvas, probe the electric potential and field at any location, and watch equipotential contour lines and field arrows update in real time. Record measurements to verify the relationship between electric field and potential.

Guided Experiment: Mapping a Dipole Field

For two equal and opposite charges, what do you predict the potential and field will look like along the axis connecting them? What about along the perpendicular bisector?

Write your hypothesis in the Lab Report panel, then click Next.

Field Visualization

Click to probe potential and field. Drag charges to reposition.

Positive chargeNegative chargeProbe pointV > 0V < 0

Controls

(-3, 0)µC

Probe Results

Click on the canvas to probe the electric potential and field at any point.

Data Table

(0 rows)
#Trialx(cm)y(cm)V(V)|E|(V/m)Ex(V/m)Ey(V/m)θ(°)
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0 / 500
0 / 500

Reference Guide

Coulomb's Law

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

F=kq1q2r2k=8.99×109  N⋅m2/C2F = k \frac{q_1 q_2}{r^2} \qquad k = 8.99 \times 10^9 \; \text{N} \cdot \text{m}^2/\text{C}^2

The electric potential from a single point charge is the scalar quantity V = kq/r, where r is the distance from the charge. Unlike force and field, potential does not have a direction.

Superposition of Potentials

The total potential at any point is the algebraic (scalar) sum of potentials from each individual charge. No vector addition is needed.

Vtotal=∑ikqiriV_{\text{total}} = \sum_i \frac{k q_i}{r_i}

This makes potential calculations simpler than field calculations, since potentials add as plain numbers while fields must be added as vectors.

Electric Field from Potential

The electric field is the negative gradient of the potential. The field points in the direction of steepest decrease in V.

E⃗=−∇VEx=−∂V∂x,  Ey=−∂V∂y\vec{E} = -\nabla V \qquad E_x = -\frac{\partial V}{\partial x}, \; E_y = -\frac{\partial V}{\partial y}

Along a line, this simplifies to E ≈ -ΔV/Δr. You can verify this relationship by probing the potential at two nearby points and comparing -ΔV/Δr to the measured |E|.

Equipotential Lines

Equipotential lines connect points of equal potential. No work is done moving a charge along an equipotential because the potential difference is zero.

Equipotential lines are always perpendicular to electric field lines. Around a single point charge, they form concentric circles. For a dipole, the perpendicular bisector is the V = 0 equipotential.

Field lines are closer together where the field is stronger, and equipotential lines are closer together where the potential changes rapidly.