# magnetic field

(noun)

## Definition of magnetic field

A condition in the space around a magnet or electric current in which there is a detectable magnetic force, and where two magnetic poles are present.

Source: Wiktionary - CC BY-SA 3.0

## Examples of magnetic field in the following topics:

• ### Magnetic Field Lines

• Since magnetic forces act at a distance, we define a magnetic field to represent magnetic forces.
• A pictorial representation of magnetic field lines is very useful in visualizing the strength and direction of the magnetic field .
• The magnetic field is traditionally called the B-field.
• The properties of magnetic field lines can be summarized by these rules: The direction of the magnetic field is tangent to the field line at any point in space.
• If magnetic monopoles existed, then magnetic field lines would begin and end on them.
• Magnetic field lines are useful for visually representing the strength and direction of the magnetic field.
• ### Energy Stored in a Magnetic Field

• When a conductor carries a current, a magnetic field surrounding the conductor is produced.
• The resulting magnetic flux is proportional to the current.
• For an inductor, that outlet is the magnetic field—the energy stored by an inductor is equal to the work needed to produce a current through the inductor.
• From Eq. 1, the energy stored in the magnetic field created by the solenoid is: $E = \frac{1}{2} LI^2 = \frac{1}{2} \frac{\mu N^2 A}{L} \frac{B^2 L^2}{\mu^2 N^2} = \frac{B^2}{2\mu}~AL$.
•  Therefore, the energy density $u_B = energy / volume$ of a magnetic field B is written as $u_B = \frac{B^2}{2\mu}$.
• In an inductor, energy is stored within a magnetic field.
• ### Helical Motion

• In this case, the magnetic force is also perpendicular to the velocity (and the magnetic field vector, of course) at any given moment resulting in circular motion.
• quickly reviews this situation in the case of a negatively charged particle in a magnetic field directed into the page.What if the velocity is not perpendicular to the magnetic field?
• shows how electrons not moving perpendicular to magnetic field lines follow the field lines.
• Some cosmic rays, for example, follow the Earth’s magnetic field lines, entering the atmosphere near the magnetic poles and causing the southern or northern lights through their ionization of molecules in the atmosphere.
• Those particles that approach middle latitudes must cross magnetic field lines, and many are prevented from penetrating the atmosphere.
• Helical motion results when the velocity vector is not perpendicular to the magnetic field vector.
• ### Paramagnetism and Diamagnetism

• The magnetic moment induced by the applied field is linear in the field strength; it is also rather weak.
• When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field.
• These materials are slightly attracted by a magnetic field and the material does not retain the magnetic properties when the external field is removed, as illustrated in .
• Diamagnetism Diamagnetism is the property of an object or material that causes it to create a magnetic field in opposition to an externally applied magnetic field.
• The eddy currents then produce an induced magnetic field opposite the applied field, resisting the conductor's motion.
• Paramagnetism is the attraction of material while in a magnetic field, and diamagnetism is the repulsion of magnetic fields.
• ### Energy in a Magnetic Field

• Energy is needed to generate a magnetic field both to work against the electric field that a changing magnetic field creates and to change the magnetization of any material within the magnetic field.
• For non-dispersive materials this same energy is released when the magnetic field is destroyed.
• Therefore, this energy can be modeled as being "stored" in the magnetic field .Energy Stored in a Magnetic FieldFor linear, non-dispersive, materials (such that B = μH where μ, called the permeability, is frequency-independent), the  energy density is: $u = \frac{\mathbf{B}\cdot\mathbf{B}}{2\mu} = \frac{\mu\mathbf{H}\cdot\mathbf{H}}{2}$.
• For hysteretic materials such as ferromagnets and superconductors, the work needed also depends on how the magnetic field is created.
• For linear non-dispersive materials, though, the general equation leads directly to the simpler energy density equation given above.Energy Stored in the Field of a Solenoid The energy stored by an inductor is equal to the amount of work required to establish the current through the inductor, and therefore the magnetic field.
• Magnetic field stores energy.
• ### Electric Currents and Magnetic Fields

• Electric Current and Magnetic FieldsElectric current produces a magnetic field.
• This magnetic field can be visualized as a pattern of circular field lines surrounding a wire.
• This is one of the simplest cases to calculate the magnetic field strenght from a current.
•  The magnetic field of a long straight wire has more implications than one might first suspect.
• A current-carrying wire feels a force in the presence of a magnetic field.
• An electric current will produce a magnetic field, which can be visualized as a series of circular field lines around a wire segment.
• ### Ampere's Law: Magnetic Field Due to a Long Straight Wire

• Current running through a wire will produce both an electric field and a magnetic field.
• For a closed curve of length C, magnetic field (B) is related to current (IC) as in Ampere's Law, stated mathematically as:$\oint_C {Bd\ell = \mu _0 I_C }$In this equation, dl represents the differential of length of wire in the curved wire, and μ0 is the permeability of free space.
• For a short, straight length of conductor (typically a wire) this law generally calculates partial magnetic field (dB) as a function of current for an infinitesimally small segment of wire (dl) at a point r distance away from the conductor:$d {\bf B}=\frac {\mu_0}{4 \pi} \frac {Id{\bf l} \times {\bf r}}{r^3}$.In this equation, the r vector can be written as r̂ (the unit vector in direction of r), if the r3 term in the denominator is reduced to r2 (this is simply reducing like terms in a fraction).
• Integrating the previous differential equation, we find:${\bf B}=\frac {\mu_0}{4 \pi} \oint_C {\frac {Id{\bf l} \times {\bf \hat{r}}}{r^2}}$.This relationship holds for constant current in a straight wire, in which magnetic field at a point due to all current elements comprising the straight wire is the same.
• As illustrated in  the direction of the magnetic field can be determined using the right hand rule—pointing one's thumb in the direction of current, the curl of one's fingers indicates the direction of the magnetic field around the straight wire.
• Current running through a wire will produce a magnetic field that can be calculated using the Biot-Savart Law.
• ### Permanent Magnets

• Permanent Magnets Overview Recall that a magnet is a material or object that generates a magnetic field.
• Types of Magnets A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field .
• Although ferromagnetic materials are the only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism.
• However, before magnetization these regions are small and randomly oriented throughout the unmagnetized ferromagnetic objects, so there is no net magnetic field.
• In response to an external magnetic field like the one applied in the above figure, these regions grow and become aligned.
• Permanent magnets are objects made from ferromagnetic material that produce a persistent magnetic field.
• ### The Hall Effect

• The Hall effect is the phenomenon in which a voltage difference (called the Hall voltage) is produced across an electrical conductor, transverse to the conductor's electric current when a magnetic field perpendicular to the conductor's current is applied.When a magnetic field is present that is not parallel to the motion of moving charges within a conductor, the charges experience the Lorentz force.
• In the absence of such a field, the charges follow a roughly straight path, occasionally colliding with impurities.In the presence of a magnetic field with a perpendicular component, the paths charges take becomes curved such that they accumulate on one face of the material.
• This opposes the magnetic force, eventually to the point of cancelation, resulting in electron flow in a straight path .For a metal containing only one type of charge carrier (electrons), the Hall voltage (VH) can be calculated as a factor of current (I), magnetic field (B), thickness of the conductor plate (t), and charge carrier density (n) of the carrier electrons:$V_H=- \frac {IB}{net}$In this formula, e represents the elementary charge.The Hall coefficient (RH) is a characteristic of a conductor's material, and is defined as the ratio of induced electric field (Ey) to the product of current density (jx) and applied magnetic field (B):$R_H=\frac {E_y}{j_xB}=\frac {V_Ht}{IB}=-\frac {1}{ne}$The Hall effect is a rather ubiquitous phenomenon in physics, and appears not only in conductors, but semiconductors, ionized gases, and in quantum spin among other applications.
• When current runs through a wire exposed to a magnetic field a potential is produced across the conductor that is transverse to the current.
• ### Ferromagnets and Electromagnets

• Electromagnets In an electromagnet the magnetic field is produced by the flow of electric current.
• If the current disappears, the magnetic field is turned off.
• An electric current flowing in a wire creates a magnetic field around the wire.
• The magnetic field from all the turns of wire passes through the center of the coil creating a strong magnetic field there.
• Due to the high magnetic permeability μ of the ferromagnetic material, the ferromagnetic core increases the magnetic field to thousands of times the strength of the field of the coil alone.
• There are two type of magnets—ferromagnets that can sustain a permanent magnetic field, and electromagnets produced by the flow of current.