In magnetism and electromagnetism, magnetic field is a physical property of space that quantifies the magnetic influence at a given location.
Magnetic fields
deflect moving electric charges (including electric currents) apply torques on magnets to twist them in the direction of the magnetic field attract or repel magnets and magnetic material such as iron induce electric currents in electically conducting material.
Magnetic fields are created by
permanent magnetic materials moving electric charges (including electric current).
Magnetic fields are used throughout modern science and technology. In electrical engineering and electromechanics, it is important in the design and use of electric motors, generators, transformers, electromagnets, and inductors among many other devices. In material science, magnetic forces give information about the charge carriers in a material through the Hall effect in addition to other uses.
In geology and geophysics, Earth's magnetic field gives information about earth's interior while local magnetic field measurements are used in mineral exploration and other measurements. Too, Earth's magnetic field creates a magnetosphere which shields the Earth's ozone layer and the rest of the planet from the solar wind. In physics, the relationship between the magnetic and electric fields forms the field of electrodynamics which is important to understand a wide range of phenomena including light (also known as electromagnetic radiation) and the properties of antenna and transmission lines.
Since both strength and direction of a magnetic field may vary with location, it is described mathematically by assigning a vector to each point of space, making it a vector field.More precisely, magnetic field is a pseudovector field due to its properties under inversion. There are two different, but closely related, vector fields which together or separately are called "magnetic field". These are written as and . While the best names for these fields is the subject of long running debate, the underlying physics is uncontested.
Definitions
The international ISO 80000-6 standard defines magnetic field as "that component of an electromagnetic field which is characterized by the magnetic field strength vector and the magnetic flux density vector ." This standard also defines and as given in the sections below. While there is wide agreement on these definitions of and , there are many alternative names for both (see sidebars in the corresponding sections).
The B-field
Also known as magnetic flux density, the magnetic field causes magnetic forces, magnetic torques and electromagnetic induction. Therefore, it can be defined by any equation that describes these phenomena.
For example, the magnetic field vector at any point can be defined as the vector field that, when used in the Lorentz force law, correctly predicts the force on a moving charged particle at that point:
Here is the force on the particle, is the particle's electric charge, is the external electric field, , is the particle's velocity, and × denotes the cross product.
In other words,
For more details see Lorentz Force or the section below.
The SI unit of is tesla (symbol: T).The SI unit of (magnetic flux) is the weber (symbol: Wb), related to the tesla by 1 Wb/m2 = 1 T. The SI unit tesla is equal to (newton·second)/(coulomb·metre). This can be seen from the magnetic part of the Lorentz force law. The Gaussian-cgs unit of is the gauss (symbol: G). Tesla for describing a large magnetic force; gauss (tesla/10000) for describing a small magnetic force as that at the surface of earth. (The conversion is 1 T ≘ 10000 G.) One nanotesla corresponds to 1 gamma (symbol: γ).
The H-field
While creates magnetic forces and torques on objects and induces currents in conducting wires, it is not always easy to calculate. For this reason, it is useful to define a magnetic field "As it turns out, H is a more useful quantity than D. ... The reason is this: To build an electromagnet you run a certain (free) current through a coil. The current is the thing you read on the dial, and this determines H (or at any rate, the line integral of H).", also known as magnetic field strength, such that:
where is the vacuum permeability, and is the magnetization vector which represents how magnetized a given region of material is and is defined below. In a vacuum, making them equivalent to each other. Inside a material they are different.
Defined this way, can in many circumstanceThe induced component is zero for certain high-symmetry cases where Ampere's law can easily be used and is irrelevant for certain quantities such as those that depend a line integral (over a loop) of the -field such as in the MMF of magnetic circuits. be treated as if it is only due to electrical currents with corrections accounting for due to nearby magnetic material.This component of is called the demagnetizing field, or stray field In any case, still needs to be calculated from if forces, torques, induced currents, or energy changes need to be calculated.
The SI unit of is the ampere per metre (A/m) and the Gaussian unit is the oersted (Oe).
Measurement and visualization
Magnetometers
Instruments used to measure the local magnetic -field are known as a magnetometers. Important classes of magnetometers include induction magnetometers (or search-coil magnetometers) which measure only varying magnetic fields, rotating coil magnetometers, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around a field line produce synchrotron radiation that is detectable in radio waves. The finest precision for a magnetic field measurement was attained by Gravity Probe B at ().
The -field cannot be directly measured but can be inferred from the currents that create it.
Magnetic field lines
Magnetic field can be visualized by a set of magnetic field lines, that follow the direction of the field at each point. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and the local density of field lines can be made proportional to its strength. Magnetic field lines are like streamlines in fluid flow, in that they represent a continuous distribution, and a different resolution would show more or fewer lines.
Magnetic field lines have the following properties:
The direction of the magnetic field is tangent to the field line at any point. A small compass points in the direction of the field line. The strength of the field is proportional to the closeness of the lines. Magnetic field lines never cross. Magnetic field lines are directed from the north pole to the south pole.
An advantage of using magnetic field lines as a representation is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as the "number" of field lines through a surface. These concepts can then be "translated" to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field.
Different unit systems This article uses the SI unit system. But other unit systems, most importantly the Gaussian unit system (which is the most used system of cgs units for electromagnetism), are still being used in some disciplines, countries, and textbooks. The equations for each unit system can be, and often are, different for different unit systems.
Force on moving charges and current Moving electric charges including electrical currents experience a force due to magnetic fields.
Magnetic force on a charged particle
A charged particle moving in a -field experiences a sideways force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle. This force is known as the Lorentz force, and is given by:
where is the force, is the electric charge of the particle, is the instantaneous velocity of the particle, and is the magnetic field (in teslas). The direction of force on the charge can be determined by the right-hand rule (see the figure).
The Lorentz force is always perpendicular to both the velocity of the particle and the magnetic field that created it. When a charged particle moves in a static magnetic field, it traces a helical path in which the helix axis is parallel to the magnetic field, and in which the speed of the particle remains constant.
Force on current-carrying wire
When a wire carrying a steady electric current is placed in an external magnetic field, each of the moving charges in the wire experience the Lorentz force. Together, these forces produce a net macroscopic force on the wire. This force (on a macroscopic current) is often referred to as the Laplace force.
For a straight, stationary wire in a uniform magnetic field, this force is given by:
where is the current and is a vector whose magnitude is the length of the wire, and whose direction is along the wire, aligned with the direction of the current.
If the wire is not straight or the magnetic field is non-uniform, the total force can be computed by applying the formula to each infinitesimal segment of wire , then adding up all these forces by integration. In this case, the net force on a stationary wire carrying a steady current is
This force creates an attractive/repulsive force between 2 parallel wires as the current through each produces a magnetic field that pushes/pulls on the other. Too, a loop of current in a magnetic field will experience a torque due to the different direction of the force on different sides of the loop as describe in the next section.
Net force and torque on current loops
A magnetic field acting on a current carrying loop produces both a torque and a net force (if the magnetic field is non-uniform). This effect is important for driving certain types of motors and in modeling forces and torques on atoms.
Calculating the torque on a rectangular loop is straightforward. The diagram to the right shows a rectangular loop of current in a uniform magnetic field (with a direction indicated by the green arrows). For simplicity the loop is aligned so that it is along the direction of the magnetic field. The magnetic force on opposite sides of the loop are equal and opposite producing no net force on the loop. The forces on the short sides (here shown as violet arrows), though, produce a net torque equal to the product of the force and the perpendicular distance between them. Denoting the short side length as , the magnitude of that force is = using the equation for the magnetic force on a straight wire given in the previous section. The magnitude of the net torque (along dashed axis) is therefore = . Using the fact that the area = and generalizing for all angles gives
Here the direction of the area is the normal to the area as determined by the right hand grip rule of the current loop. While derived for a rectangular loop this equation is valid for a flat loop of any shape and orientation. As described above, there is no net force on a loop in a uniform magnetic field. However, non-uniform magnetic fields do produce a net force. This net force tends to pull the object in direction of the stronger magnetic field.
Net force and torque on a magnetic dipole
Since the net force on a loop is proportional to the current of the loop times it area, it is natural to define a quantity called the magnetic dipole moment such that
For a sufficiently small current loop, the details of the current loop such as it shape, area, orientation, and current around the loop are all hidden in and otherwise do not matter. Such loops are called magnetic dipoles. All magnetic dipoles with the same dipole moment are affected the same way.