Search results
Results from the WOW.Com Content Network
Lorentz force on a charged particle (of charge q) in motion (velocity v), used as the definition of the E field and B field. Here subscripts e and m are used to differ between electric and magnetic charges .
The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c 2). Because the speed of light is a large number in everyday units (approximately 300 000 km/s or 186 000 mi/s), the formula implies that a small amount of mass corresponds to an enormous amount of energy.
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
Thus the formula for this electromagnetic energy–mass relation is m e m = 4 3 E e m c 2 {\displaystyle m_{\mathrm {em} }={\frac {4}{3}}{\frac {E_{\mathrm {em} }}{c^{2}}}} This was discussed in connection with the proposal of the electrical origin of matter, so Wilhelm Wien (1900), [ 9 ] and Max Abraham (1902), [ 6 ] came to the conclusion ...
is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇ 2 is the Laplace operator. In a vacuum, v ph = c 0 = 299 792 458 m/s, a fundamental physical constant. [1] The electromagnetic wave equation derives from Maxwell's equations.
Einstein Triangle. The energy–momentum relation is consistent with the familiar mass–energy relation in both its interpretations: E = mc 2 relates total energy E to the (total) relativistic mass m (alternatively denoted m rel or m tot), while E 0 = m 0 c 2 relates rest energy E 0 to (invariant) rest mass m 0.
A phasor such as E m is understood to signify a sinusoidally varying field whose instantaneous amplitude E(t) follows the real part of E m e jωt where ω is the (radian) frequency of the sinusoidal wave being considered. In the time domain, it will be seen that the instantaneous power flow will be fluctuating at a frequency of 2ω.
The net electric flux Φ E is the surface integral of the electric field E passing through Σ: =, The net electric current I is the surface integral of the electric current density J passing through Σ : I = ∬ Σ J ⋅ d S , {\displaystyle I=\iint _{\Sigma }\mathbf {J} \cdot \mathrm {d} \mathbf {S} ,} where d S denotes the differential vector ...