The magnetic field is the physical disturbance that appears around moving charges and electric currents.
Until 1820, electricity and magnetism were separate sciences. Magnetism was believed to be an exclusive property of certain stones (like magnetite). But Hans Christian Ørsted changed history by observing that a compass needle deflected when passing near a current-carrying wire.
He discovered a fundamental truth: “magnetic charges” do not exist. Magnetism is, in reality, a manifestation of electricity in motion.
The Origin: moving charges
A stationary electron generates an Electric Field (𝐸). But if that electron moves, special relativity causes the field to deform and a new force perpendicular to its motion appears. This perturbation of space is the Magnetic Field.
Biot-Savart Law (Conceptual): Every electric current (𝐼) generates a magnetic field around it in the form of concentric rings.
To determine the direction of this field, we use the Right-Hand Rule (or corkscrew rule):
- If your thumb points in the direction of the Current (𝐼).
- Your curled fingers indicate the direction of the Magnetic Field lines.
The Quantities: B or H?
In engineering, the word “Magnetic Field” is often used interchangeably for two different things. It’s time to be precise.
Magnetic Field Intensity (H)
It is the external “cause”. It depends exclusively on the geometry of the coil and the current flowing through it. It does not care what material is inside.
- Unit: Ampere-turn per meter (𝐴/𝑚).
- Formula (in a long solenoid):
(Turns x Current / Length).
Magnetic Flux Density (𝐵)
It is the actual “effect”. It is the density of force lines that actually traverse space. It determines the force a motor will feel or the voltage a transformer will generate.
- Unit: Tesla (𝑇).
The key relationship: The real field (𝐵) is the external effort (𝐻) amplified by the material (𝜇).
Magnetic Permeability (𝜇)
This is where matter comes into play. If you have an air coil and create a field 𝐻, you will have a weak field 𝐵. But if you insert an Iron core inside, the field 𝐵 multiplies by 1,000 or 5,000 times.
This happens due to Magnetic Permeability (𝜇): the ability of a material to “conduct” or concentrate magnetic field lines.
(Permeability of free space): It is a universal constant (4π · 10⁻⁷). It is the base reference. (Relative Permeability): It is the amplification factor of the material. - Vacuum/Air:
. (Does not amplify). - Copper/Plastic:
. (These are non-magnetic materials). - Iron/Steel (Ferromagnetic):
can be 500, 2,000 or 10,000.
- Vacuum/Air:
Magnetic Domains:
Why does iron amplify so much? Inside the iron, there are millions of tiny “groups” of electrons, forming atomic “mini-magnets” (electron spins). Normally they are disordered and cancel each other out.
When we apply an external field (𝐻), all these domains align in the same direction, adding their strength to yours. The material “helps” the field.
Magnetic Flux
Finally, if 𝐵 is the density (how many lines per square meter), we need a quantity for the total amount of magnetism passing through a surface.
That is Magnetic Flux (𝛷).
-
Unit: Weber (𝑊𝑏).
-
Analogy:
- (Teslas) is the intensity of the rain (drops per m²).
- 𝛷 (Webers) is the total water you collect in a bucket of surface area 𝑆.
