What is the electric potential 1 m from a +2 μC point charge?

You can work it out this way: use V = kq/r with k = 8.99 × 10⁹ N·m²/C².

What is the geometric relationship between equipotential lines and electric field lines?

You can work it out this way: think about the direction of E = −∇V.

How much work is needed to move a +1 μC charge from V = 100 V to V = 300 V?

You can work it out this way: use W = q(V₁ − V₂) and be careful about the sign of work.

Pro 🔒~25 min

Electric Potential & Voltage

Map equipotential surfaces and understand work done by electric fields

How it works

Electric potential V at a point is the work done per unit positive charge to bring a test charge from infinity to that point. For a point charge, V = kq/r, and the field points in the direction of decreasing potential: E = −ΔV/Δx. Equipotential lines connect points of equal potential; they are always perpendicular to electric field lines. No work is done moving a charge along an equipotential surface.

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Step-by-step

Adjust the source charge value and sign with the sliders to reshape the potential map.
Click anywhere on the canvas to read the local potential.
Unlock Pro mode to add a second or third charge and observe how their fields superpose.

Key formulas

$V = \frac{kq}{r} \quad (k = 8.99 \times 10^9\,\text{N}\cdot\text{m}^2\text{/C}^2)$ Electric potential due to a point charge
$E = -\frac{\Delta V}{\Delta x}$ Electric field from potential gradient
$U = qV$ Electric potential energy
$W = q(V_1 - V_2)$ Work done by the electric field

Frequently asked questions

What is the electric potential 1 m from a +2 μC point charge?: You can work it out this way: use V = kq/r with k = 8.99 × 10⁹ N·m²/C².
What is the geometric relationship between equipotential lines and electric field lines?: You can work it out this way: think about the direction of E = −∇V.
How much work is needed to move a +1 μC charge from V = 100 V to V = 300 V?: You can work it out this way: use W = q(V₁ − V₂) and be careful about the sign of work.