Draw the Field: Charges and Electric Field Lines

How to use this simulation

1. Pick an arrangement: a single charge, a dipole, two like charges or four charges.
2. Drag any charge and the field lines are redrawn instantly. Double-click a charge to remove it.
3. Click a charge to select it, then change its size with the slider: the number of lines changes with it.
4. Hover or touch anywhere: the field strength, its direction and the potential V at that point appear in the readings panel.
5. Press ▶ to release the orange +1 nC test charge and watch where the field pushes it.

Why does a balloon stick to the wall?

Rub a balloon on your hair a few times and hold it near your head: your hair stands up and reaches for it. Put it against a wall and it just stays there. Nothing is glued, nothing is touching your hair, and yet there is clearly a force.

The small shock you get from a door handle after walking on carpet, the crackle when you pull off a wool jumper in winter, and a lightning bolt splitting a stormy sky are all the same story at different sizes. In each case, electric charge has built up somewhere and is pulling or pushing on other charges.

Behind every one of these is an invisible zone of influence around the charge: the electric field. This page makes that invisible thing visible, then shows step by step how physicists measure it.

Starting from zero: charge and field

Everything is made of atoms, and atoms contain positive protons and negative electrons. Normally the two balance, so objects are neutral. Rubbing a balloon on hair moves a few electrons from your hair to the balloon: the balloon becomes negatively charged and your hair positively charged. Charge is measured in coulombs (C).

Now think about gravity. The Earth pulls you down without touching you, because it is surrounded by a gravitational field. A magnet grabs a paper clip from a distance because it has a magnetic field. In the same way, every charge changes the space around it, and any other charge that wanders into that space feels a force.

That region of influence is the electric field. A friendly picture: when a loud speaker is playing, you can hear it anywhere in the room, loudest right next to it and fainter by the door. The electric field is like that, strong near the charge and weaker far away.

There is only one rule for how charges treat each other: like charges repel, unlike charges attract. Two positives push apart; a positive and a negative pull together.

Words you will keep meeting

Here are the key terms in one place, so nothing trips you up later:

From Coulomb's law to field intensity

To put a number on the field, you first need the force between two charges. That is exactly what Coulomb's law gives.

Field lines: a picture of the invisible

You cannot see a field, so Michael Faraday came up with a brilliant trick: draw imaginary lines so that the tangent at any point shows the direction of E there. These are electric field lines, and the lines drifting in the simulation above are calculated exactly this way.

Rather than memorising the properties, learn why each one is true. Then you will never forget them:

• Field lines start on positive charges and end on negative charges, because a positive test charge moves away from positive and towards negative.
• Two field lines never cross. If they did, the crossing point would have two tangents, meaning two directions of E at one point, which is impossible.
• Where lines are crowded the field is strong; where they spread out it is weak. That is why lines bunch up near a charge and thin out far away.
• Field lines meet a conductor's surface at right angles. A slanted line would have a component along the surface, and charges would slide around.
• Field lines from static charges never form closed loops. This is a big difference from magnetic field lines.
• A bigger charge has more lines leaving or entering it.

Is electric field the same as electric potential?

No, and examiners love this question. Field intensity tells you how hard, and in which direction, a unit charge gets pushed. Potential tells you how much work it takes to bring a unit charge there. Think of a hill: the potential is the height of a spot, the field is how steep the slope is.

Try it yourself in the simulation

When you finish reading, go back up and try these one by one. Each one proves a textbook rule in front of your eyes.

• Choose "Single positive" and move the pointer from near the charge to far away. Watch E fall in the readings panel. Does doubling the distance cut it to about a quarter?
• Choose "Dipole (+ and −)" and hover exactly halfway between the charges. E is not zero, and it points from + to −.
• Choose "Two like charges" and hunt for the middle. Somewhere E drops almost to zero: that is the neutral point.
• Click a charge and raise its size. More field lines leave it.
• Press ▶ and watch the orange test charge speed up as it heads towards the negative charge.

Solved problems, step by step

All of these use k = 9 × 10⁹ N m² C⁻². Always convert to SI units first: multiply µC by 10⁻⁶ to get coulombs and turn cm into m. Most wrong answers come from skipping this.

Mistakes almost everyone makes

These turn up in exam scripts again and again, so spot them now:

• Plugging in µC without converting to C, which makes the answer a million times too big.
• Forgetting to square r, or squaring it in the potential formula where it should not be.
• Adding the fields of several charges as plain numbers and ignoring direction. E is a vector; potential is a scalar.
• Drawing the force on an electron in the same direction as E.
• Treating a field line as the path a test charge must follow. Field lines show the force, not the velocity.

Electric fields in real life

The electric field is not just a textbook idea. It is at work all around you:

• Lightning conductors: a pointed metal rod on top of a tall building, connected to the ground by a thick wire, gives a lightning strike an easy path to earth instead of through the walls.
• Photocopiers and laser printers: light arranges charge on a drum in the shape of the page, and powdered toner sticks only where the charge is.
• Electrostatic precipitators: factory chimneys charge the dust in smoke and then pull it onto oppositely charged plates, so far less dust escapes into the air.
• Safety in a car: during a thunderstorm you are relatively safe inside a car with a metal roof, because the charge travels over the outer metal shell. This is a Faraday cage.
• Spray painting: paint droplets are charged so they are pulled evenly onto the metal body of a car, wasting less paint.

Exam corner

Questions on this topic tend to come in a few familiar shapes. Here is what examiners usually ask, with the core of a good answer.

The whole topic at a glance

If you only have five minutes before an exam, read this:

• Electric field: the region around a charge where another charge feels a force.
• Coulomb's law: F = kq₁q₂/r², with k ≈ 9 × 10⁹ N m² C⁻².
• Field intensity: E = F/q₀ = kq/r², a vector, unit N C⁻¹ = V m⁻¹.
• Potential: V = kq/r, a scalar, unit volt.
• Field lines run from + to −, never cross, and are crowded where the field is strong.
• For several charges: add fields as vectors, add potentials as numbers.

Frequently asked questions