How to use it
The canvas is a flat slice of space in which one grid square is 10 cm. Red discs are positive point charges, blue discs are negative ones, and the number on each disc is its charge in nanocoulombs (nC). Start with a preset, or pick Add + or Add − and tap the canvas to drop a charge. Drag any charge and the picture follows: black field lines with arrows, thin equipotential lines and a colour map of the potential, red where it is positive and blue where it is negative.
Point at any spot to read the field strength E, its direction and the potential V there. To see how a charge would move, choose Test charge, press on a starting point and let go. The small green charge starts at rest and leaves a trail.
Controls
- Mouse: drag a charge to move it, click empty space to use the selected tool, right-click a charge to remove it. Hovering shows E and V.
- Touch: drag charges with a finger. In Measure mode, slide over empty space to read the values. The page does not scroll while your finger is on the canvas.
- Keyboard (canvas focused): arrow keys move the measuring point, or the selected charge, by 1 cm (5 cm with Shift). P and N add a charge, [ and ] select one, + and − resize it, F flips its sign, Delete removes it, Escape deselects. T releases the test charge at the measuring point, Space pauses it, R resets it.
- Charge size: the slider sets 1 to 9 nC for the selected charge and for new ones.
- Display: switch the layers on or off, and set the lines per nanocoulomb and the voltage step between equipotentials.
How it works
Coulomb’s law says that two point charges q1 and q2 a distance r apart push or pull each other with a force
Like charges repel and opposite charges attract. The electric field is the force per unit of charge that a small test charge would feel, so a single point charge q creates
The field points away from a positive charge and toward a negative one. It is measured in volts per metre, the same as newtons per coulomb. The potential V, in volts, is the energy per unit of charge, counted as zero far away. For example, 1 nC produces about 900 V/m and 90 V at a distance of 10 cm.
With several charges the superposition principle applies: the total field is the vector sum of the separate fields, and the total potential is the plain sum of the separate potentials.
A field line is a curve that follows the direction of E everywhere. The program starts lines evenly around each positive charge, a fixed number per nanocoulomb, and follows the field in small steps (fourth-order Runge–Kutta) until the line reaches a negative charge or leaves the area. An equipotential joins points with the same V, like a contour line on a map. Moving a charge along it takes no work, so the field has no component along it: field lines always cross equipotentials at right angles, pointing from high potential to low. Where equipotentials crowd together, the field is strong.
The test charge has ±1 nC and a mass of 1 mg; its acceleration is a = qE / m. It is treated as too small to disturb the other charges.
Things to try
- Load Single charge and measure 10 cm and 20 cm away from it. Doubling the distance cuts E to a quarter and V to a half.
- In the Dipole preset, measure halfway between the charges. The potential is zero there, yet the field is about 900 V/m, pointing from plus to minus.
- In Two like charges the midpoint is the opposite case: the field is zero but the potential is about 180 V.
- Make one charge of the dipole larger. Some of its lines now find no partner and run off to infinity.
- Load Capacitor. Between the rows the field lines run almost parallel and the equipotentials are nearly flat, as inside a parallel-plate capacitor. Rows of point charges are not real plates, though, so the field still grows stronger toward each row.
- Release a test charge beside a dipole and compare its trail with the field lines.
Frequently asked questions
Can two field lines cross?
No. At a crossing the field would have two directions at once. Lines can only meet at a charge or at a point where the field is zero.
Why are field lines and equipotentials perpendicular?
The field points the way the potential falls fastest. Along an equipotential the potential does not change at all, so the field has no component in that direction.
Does the number of lines mean anything?
It is a drawing convention: the lines leaving a positive charge are proportional in number to its size. A flat picture of a three-dimensional field cannot show strength exactly through line spacing, so use the readout for real values.
Why does the test charge leave its field line?
The field sets the acceleration, not the velocity. Once the charge is moving, inertia carries it straight on where the line bends. A charge released from rest follows a field line only if that line is straight.