How to play Potential Map
- Choose a test and read the charges and the path on the card.
- Use V = k·Q ÷ r for each charge, add the potentials, and W = q·(V₂ − V₁) for the work.
- Type your prediction and press Start. The test charge is carried along the path; its meter reads V and the work.
- Compare the meter, the contours, and the graph with your orange prediction.
Electric potential
The electric potential at a point is the energy each coulomb of charge has there: V = U ÷ q, in volts, where one volt is one joule per coulomb. A point charge Q makes V = k·Q ÷ r, which falls as 1 ÷ r rather than 1 ÷ r² like the field. Potential is a plain number with a sign, so the potentials of several charges simply add: between two positive charges they never cancel, even where the fields do, and between a + and a − charge of the same size the potential halfway is 0, even though the field there is strong. A map of potential looks like a hill map: near a positive charge the ground is high, and contour lines join points at the same potential. Carrying a charge q from one point to another takes work W = q·(V₂ − V₁), whatever path you take, and walking along a contour takes none, because the electric force always points straight across the contours.
A focused learning model
The fixed charges are point charges in air, treated as vacuum, with the potential taken as 0 far away. The +1 nC test charge is carried steadily along the path for 2 s and held for 1 s; it is too small to move the other charges, and its meter leaves out its own potential. The work counter shows q·(V now − V at the start), the work you do against the electric force, whatever the path. Shading goes from navy at 0 V to lighter at 300 V and above; contour rings are drawn every 20 V once a run starts, and the force arrow is to a stated scale. Answers within 2% are right; a work of 0 must be within 0.5 nJ.