Magnetic field
where Fmagnetic, v, and B are the scalar magnitude of their respective vectors, and θ is the angle between the velocity of the particle and the magnetic field.
In other words,[10]: 173–4 [T]he command, "Measure the direction and magnitude of the vector B at such and such a place," calls for the following operations: Take a particle of known charge q.
For instance, electrons spiraling around a field line produce synchrotron radiation that is detectable in radio waves.
If m is in the same direction as B then the dot product is positive and the gradient points "uphill" pulling the magnet into regions of higher B-field (more strictly larger m · B).
[20] Magnetic field lines form in concentric circles around a cylindrical current-carrying conductor, such as a length of wire.
Bending a wire into multiple closely spaced loops to form a coil or "solenoid" enhances this effect.
A device so formed around an iron core may act as an electromagnet, generating a strong, well-controlled magnetic field.
In general, the incremental amount of work per unit volume δW needed to cause a small change of magnetic field δB is:
Maxwell's Equations together with the Lorentz force law form a complete description of classical electrodynamics including both electricity and magnetism.
This integral formulation of Faraday's law can be converted[note 13] into a differential form, which applies under slightly different conditions.
This additional term is proportional to the time rate of change of the electric flux and is similar to Faraday's law above but with a different and positive constant out front.
To circumvent this problem, H and D fields are used to re-factor Maxwell's equations in terms of the free current density Jf:
This is analogous to the way that special relativity mixes space and time into spacetime, and mass, momentum, and energy into four-momentum.
In advanced topics such as quantum mechanics and relativity it is often easier to work with a potential formulation of electrodynamics rather than in terms of the electric and magnetic fields.
Maxwell's equations when expressed in terms of the potentials in Lorenz gauge can be cast into a form that agrees with special relativity.
[40] In relativity, A together with φ forms a four-potential regardless of the gauge condition, analogous to the four-momentum that combines the momentum and energy of a particle.
However, it is not able to make experimentally observed predictions such as spontaneous emission process or Lamb shift implying the need for quantization of fields.
The most accurate modern description of the electromagnetic interaction (and much else) is quantum electrodynamics (QED),[42] which is incorporated into a more complete theory known as the Standard Model of particle physics.
By continuously switching the electric current through each of the electromagnets, thereby flipping the polarity of their magnetic fields, like poles are kept next to the rotor; the resultant torque is transferred to the shaft.
This inequality would cause serious problems in standardization of the conductor size and so, to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference.
In 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin and Tesla gained U.S. patent 381,968 for his work.
It is used as well to find the sign of the dominant charge carriers in materials such as semiconductors (negative electrons or positive holes).
This result is similar in form to Ohm's law J = σE, where J is the current density, σ is the conductance and E is the electric field.
As of October 2018[update], the largest magnetic field produced over a macroscopic volume outside a lab setting is 2.8 kT (VNIIEF in Sarov, Russia, 1998).
[48][49] As of October 2018, the largest magnetic field produced in a laboratory over a macroscopic volume was 1.2 kT by researchers at the University of Tokyo in 2018.
[53][note 14] Almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth is a magnet.
[54]: 59 Building on this force between poles, Siméon Denis Poisson (1781–1840) created the first successful model of the magnetic field, which he presented in 1824.
[54]: 189–192 Later, Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law.
[54]: 222 In the process, he introduced the magnetic vector potential, which was later shown to be equivalent to the underlying mechanism proposed by Faraday.
Albert Einstein, in his paper of 1905 that established relativity, showed that both the electric and magnetic fields are part of the same phenomena viewed from different reference frames.
