Magnetic field

A magnetic field is a physical field that describes the magnetic influence on moving electric charges, electric currents,[1]: ch1 [2] and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field.[1]: ch13 [3]: 278  A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field).

In electromagnetics, the term magnetic field is used for two distinct but closely related vector fields denoted by the symbols B and H. In the International System of Units, the unit of B, magnetic flux density, is the tesla (in SI base units: kilogram per second2 per ampere),[4]: 21  which is equivalent to newton per meter per ampere. The unit of H, magnetic field strength, is ampere per meter (A/m).[4]: 22  B and H differ in how they take the medium and/or magnetization into account. In vacuum, the two fields are related through the vacuum permeability, ; in a magnetized material, the quantities on each side of this equation differ by the magnetization field of the material.

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.[5][1]: ch1  Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force, one of the four fundamental forces of nature.

Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

The force on an electric charge depends on its location, speed, and direction; two vector fields are used to describe this force.[1]: ch1  The first is the electric field, which describes the force acting on a stationary charge and gives the component of the force that is independent of motion. The magnetic field, in contrast, describes the component of the force that is proportional to both the speed and direction of charged particles.[1]: ch13  The field is defined by the Lorentz force law and is, at each instant, perpendicular to both the motion of the charge and the force it experiences.

A solenoid (electromagnet), a coil of wire with an electric current through it
The shape of the magnetic fields of a permanent magnet and an electromagnet are revealed by the orientation of iron filings sprinkled on pieces of paper
Finding the magnetic force
A charged particle that is moving with velocity v in a magnetic field B will feel a magnetic force F. Since the magnetic force always pulls sideways to the direction of motion, the particle moves in a circle.
Since these three vectors are related to each other by a cross product, the direction of this force can be found using the right hand rule.
Visualizing magnetic fields
Left: the direction of magnetic field lines represented by iron filings sprinkled on paper placed above a bar magnet.
Right: compass needles point in the direction of the local magnetic field, towards a magnet's south pole and away from its north pole.
The Amperian loop model
A current loop (ring) that goes into the page at the x and comes out at the dot produces a B-field (lines). As the radius of the current loop shrinks, the fields produced become identical to an abstract "magnetostatic dipole" (represented by an arrow pointing to the right).
Torque on a dipole
In the pole model of a dipole, an H field (to right) causes equal but opposite forces on a N pole (+q) and a S pole (−q) creating a torque.
Equivalently, a B field induces the same torque on a current loop with the same magnetic dipole moment.