Magnetic flux
Φ = B · S
| Quantity | Symbol | Unit |
|---|---|---|
| Flux | Φ | Wb |
| Magnetic flux density | B | T |
| Area | S | m² |
Elec Class
learn electricity hands-on
Lesson · chapter 10 of 15
A magnet or an electric current creates a magnetic field B around it, measured in teslas; a wire carrying a current in this field feels a force, the Laplace force F = B × I × l. It's the principle behind every electric motor.
The result is worked out before your eyes, line by line, just like on the board.
1I'm looking for
2I enter the known values
Formula used F = B · I · l
3The result
Force F120 mN
In a field of 800 mT, a conductor of length 50 mm carrying 3 A and perpendicular to the field feels a force of 120 mN.
The definition, the key points to remember and everyday examples.
A magnet has two poles, north and south: like poles repel. Field lines leave from the north and enter at the south. The field is described by the flux density B (teslas); the flux Φ = B·S (webers) measures what crosses a surface.
A current creates a field: a coil of N turns behaves like a magnet (right-hand rule: fingers follow the current, the thumb gives north). A conductor carrying I in a field B experiences the Laplace force F = B·I·l (three-finger rule).
A magnetic field is like the wind: invisible, it has a strength and a direction at every point, which field lines draw like the arrows on a weather map. A wire carrying a current is pushed by it like a sail, all the harder as the field (B), the current (I) and the length of wire (l) increase. Where it falls short: the wind pushes in its own direction, whereas the Laplace force is perpendicular to both the field and the wire.
| Quantity | Symbol | Unit |
|---|---|---|
| Flux | Φ | Wb |
| Magnetic flux density | B | T |
| Area | S | m² |
| Quantity | Symbol | Unit |
|---|---|---|
| Vacuum permeability (4π × 10⁻⁷) | µ₀ | T·m/A |
| Number of turns | N | - |
| Length | l | m |
| Quantity | Symbol | Unit |
|---|---|---|
| Force | F | N |
| Current | I | A |
| Conductor length | l | m |
Four steps to solve a problem, then an example solved line by line.
Draw the field B, the conductor and the direction of the current; note the angle between the wire and the field lines.
Lengths in meters (cm, mm), field in teslas (1 mT = 0.001 T), areas in m² (1 cm² = 10⁻⁴ m²).
F = B × I × l if the wire is perpendicular to the field; for an angle α between the wire and the field, F = B × I × l × sin α.
Right hand: the thumb follows the current, the index finger follows the field, the middle finger gives the force. Check that F is perpendicular to the wire and to the field.
A long coil of 500 turns and 20 cm carries 2 A: what flux density B inside it (µ₀ = 4π × 10⁻⁷)? A 10 cm conductor carrying 5 A is placed perpendicular to a 0.5 T field: what force?
B = µ₀ · N · I / l = 4π × 10⁻⁷ × 500 × 2 / 0.20 = 6.3 × 10⁻³ T (6.3 mT), the length being in metres.
F = B · I · l = 0.5 × 5 × 0.10 = 0.25 N, perpendicular to the conductor and to the field (three-finger rule).
The tesla (T); it is also called magnetic flux density. It's a large unit: the Earth's field is about 50 µT, a fridge magnet a few millitesla, a neodymium magnet a few hundred millitesla near its surface.
With the right hand: thumb in the direction of the current, index finger in the direction of the field, and the middle finger gives the direction of the force. Reversing the current or the field reverses the force; reversing both leaves it unchanged.
It's the amount of field passing through a surface: Φ = B × S, in webers, when the field is perpendicular to the surface. A 10 cm² loop in 0.2 T: Φ = 0.2 × 10 × 10⁻⁴ = 2 × 10⁻⁴ Wb.
Iron channels and strengthens the field: for the same current, B can be hundreds to thousands of times larger than with an air-core coil. Iron saturates, though, at around 1.5 to 2 T: beyond that, increasing the current adds almost nothing.
Each wire creates a magnetic field in which the other feels a Laplace force: two currents in the same direction attract, two currents in opposite directions repel. The old definition of the ampere was based on this effect.
Yes: heat, knocks or a strong opposing field can demagnetize it. Iron loses all magnetism above 770 °C (the Curie temperature), and many neodymium magnets weaken from 80 °C.
A permanent magnet keeps its field by itself; an electromagnet is a coil (often with an iron core) that produces a field only while a current flows through it: it can be switched, reversed, adjusted.
Towards the geographic North, which is therefore a magnetic South pole (opposite poles attract). Near a coil, the needle shows the direction of the field.
From the simplest to the most complete, each problem comes with a step-by-step solution.
Laplace rails experiment: a copper rod resting on two rails, between the arms of a U-shaped magnet, rolls as soon as a few amps flow through it. Reversing the current, then turning the magnet over, lets students check the right-hand rule.
Using Elec Class in class