Magnetic field simulation

A magnetic field simulation shows the field round a magnet as field lines, running out of the north pole and into the south pole. Our Field Lines Simulator traces the real field round bar magnets and electric charges as you drag them about, and a probe reads the field strength and direction at any point. With a magnet on the stage the probe becomes a compass that swings to line up with the field.

It opens on an electric dipole, a positive and a negative charge. Choose Bar magnet, Magnets attracting or Magnets repelling under Scenes for magnetic fields.

Try it

Field Lines Simulator

Place charges and magnets and see their electric and magnetic fields

Open the simulatorGo to its page

How to use the field simulator

1. Under Scenes, pick a starting layout: Dipole, Two alike, Unequal pair, Parallel plates, Bar magnet, Magnets attracting or Magnets repelling.
2. Under Charges and magnets, add a positive charge, a negative charge or a magnet, up to eight in all, and drag them on the stage.
3. Pick one to change it: a charge's size in nC, or a magnet's pole strength and the direction its north end points.
4. Drag the probe to read the field strength, its direction and, for charges, the potential.
5. Turn on Field lines, Equipotentials or Field vectors, and set the line density.

Under Test charge, press play to release a charge from the probe and watch the field push it. Practice and help sets questions on field strength, potential, parallel plates and the force on a charge, with worked solutions.

Magnetic field lines

Magnetic field lines show the direction a compass needle's north end would point. They leave the north pole of a magnet, curve round and enter the south pole. Where the lines are close together, the field is strong; where they spread out, it is weak.

Put the probe beside the bar magnet and read the field. The simulator's magnet, at pole strength 20 A·m, gives 1.36 mT 6 cm out along its axis from the centre and 0.126 mT at 12 cm: the field falls off quickly with distance. Above the middle of the magnet, the field points back from north to south, parallel to the magnet.

Electric field lines

An electric field line points the way a small positive charge placed there would be pushed. They start on positive charges and end on negative ones, and never cross. Equipotentials, lines of equal voltage, always cross field lines at right angles.

Example 1: the field of a point charge

For a single charge Q, the field r metres away is:

Put a single +5 nC charge on the stage and the probe 3 cm away: the simulator reads 49,944 N/C. Move the probe to 6 cm and it reads 12,486 N/C, a quarter as much, because the field follows an inverse square law. The potential at 3 cm is kQ/r = 1,498 V.

Example 2: neutral points and dipoles

In the Two alike scene, two +8 nC charges sit 10 cm apart. Halfway between them their fields are equal and opposite, so the simulator reads 0 N/C: a neutral point. In the Dipole scene, with +8 nC and −8 nC, the fields at the midpoint add up instead, giving 57,536 N/C pointing from + to −, while the potential there is 0 V.

Try one in the course, then press Mark:

Example 3: parallel plates

The Parallel plates scene puts a row of positive charges above a row of negative ones. Between them the field lines are nearly straight, parallel and evenly spaced, so the field is close to uniform, E = V/d. Near the ends the lines bulge outwards. The practice questions use E = V/d for plates.

What the simulator does not show

• No current-carrying wires or solenoids. It has bar magnets and charges only, so the circular field round a wire and the field inside a coil are not here. For the force on a wire in a field, see our Fleming's left-hand rule guide.
• Flat, two-dimensional fields. Real fields spread out in three dimensions.
• No Earth's magnetic field. The compass responds only to the magnets on the stage.

Common mistakes

• Drawing magnetic field lines from south to north. Outside a magnet they run from north to south.
• Letting field lines cross. The field has one direction at each point, so lines never cross.
• Forgetting the arrows. Field lines need arrows: N to S for magnets, + to − for charges.
• Thinking the field stops at the last line drawn. The field is everywhere; the lines are a sample of it.
• Using r in cm in E = kQ/r². Convert to metres: 3 cm is 0.03 m.

Practise fields in a short timed paper

Magnetic fields and field lines come up in High School Physics practice, and electric and magnetic fields in AP Physics 2. In the UK they appear in GCSE Physics Higher and A-level Physics: Year 2. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. Our magnetic flux guide takes field strength further.

Read next

Physics · MechanicsGravitational field strength: g, W = mg and g = GM/r²What gravitational field strength is, its value on Earth and other planets, W = mg at GCSE, g = GM/r² at A-level, field lines and worked examples.