Flux – wikipedia electricity billy elliot

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The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ. Flux is a measure of how much of the field passes through a given surface. F is decomposed into components perpendicular (⊥) and parallel ( ‖ ) to n. Only the parallel component contributes to flux because it is the maximum extent of the field passing through the surface at a point, the perpendicular component does not contribute. Top: Three field lines through a plane surface, one normal to the surface, one parallel, and one intermediate. Bottom: Field line through a curved surface, showing the setup of the unit orlando electricity providers normal and surface element to calculate flux.

Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. A flux is either a concept based in physics or used with applied mathematics. Both concepts have mathematical rigor, enabling physics c electricity and magnetism formula sheet comparison of the underlying mathematics when the terminology is unclear. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point. [1]

According to the transport definition, flux may be a single vector, or it may be a vector field / function of position. In the latter case flux can readily be integrated over a surface. By contrast, according to the electromagnetism definition, flux is the integral over a surface; it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. Thus, Maxwell’s quote only makes sense if flux is being used according to the transport definition (and furthermore is a vector field rather than single vector). This is ironic because Maxwell was one of the major developers of what we now call electric flux and magnetic flux according to the electromagnetism electricity 101 presentation definition. Their names in accordance with the quote (and transport definition) would be surface integral of electric flux and surface integral of magnetic flux, in which case electric flux would instead be defined as electric field and magnetic flux defined as magnetic field. This implies that Maxwell conceived of these fields as flows/fluxes of some sort.

Given a flux according to the electromagnetism definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the transport definition. Given a current such as electric current—charge per time, current density would also be a flux according to the transport definition—charge per time per area. Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English, all of the terms used in this paragraph are sometimes used interchangeably and ambiguously. Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, regardless of which definition of flux the term corresponds to.

In transport phenomena ( heat transfer, mass transfer and fluid dynamics), flux is defined as the rate of flow of a property gas vs electric heat per unit area, which has the dimensions [quantity]·[time] −1·[area] −1. [6] The area is of the surface the property is flowing through or across. For example, the magnitude of a river’s current, i.e. the amount of water that flows through a cross-section of the river each second, or the amount of sunlight energy that lands gas tax deduction on a patch of ground each second, are kinds of flux.

As before, the surface is assumed to be flat, and the flow is assumed to be everywhere perpendicular to it. However the flow need not be constant. q is now a function of p, a point on the surface, and A, an area. Rather than measure the total flow through the surface, q measures the flow through the disk with area A centered at p along the surface.

j ( p ) = ∂ I ∂ A ( p ) {\displaystyle \mathbf {j} (\mathbf {p} )={\frac {\partial \mathbf {I} }{\partial A}}(\mathbf {p} )} I ( A , p ) = a r g m a x n ^ n ^ p d q d t ( A , p , n ^ ) {\displaystyle \mathbf {I} (A,\mathbf {p} )={\underset {\mathbf {\hat {n}} }{\operatorname {arg\,max} }}\,\mathbf {\hat {n}} _{\mathbf {p} }{\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} ,\mathbf {\hat {n}} )}

In this case, there is no fixed surface we are measuring over. q is a function of a point, an area, and a direction (given by a unit vector, n ^ {\displaystyle \mathbf {\hat {n}} } ), and measures the flow through the electricity word search answers disk of area A perpendicular to that unit vector. I is defined picking the unit vector that maximizes the flow around the point, because the true flow is maximized across the disk that is perpendicular to it. The unit vector thus uniquely maximizes the function when it points in the true direction of the flow. [Strictly speaking, this is an abuse of notation because the arg max cannot directly compare vectors; we take the vector with the biggest norm instead.]

These direct definitions, especially the last, are rather unwieldy. For example, the argmax construction is artificial from the perspective of empirical measurements, when with a Weathervane or similar one can easily deduce the direction of flux at a point. Rather than defining the vector flux directly, it is often more intuitive to state some properties about it. Furthermore, from these properties the flux can uniquely be determined anyway.

where · is the dot product of the unit vectors. This is, the component of flux passing through the surface (i.e. normal to it) is j cos θ, while the component of flux passing tangential to the area is j sin electricity questions grade 6 θ, but there is no flux actually passing through the area in the tangential direction. The only component of flux passing normal to the area is the cosine component.

• Radiative flux, the amount of energy transferred in the form of photons at a certain distance from the source per unit area per second (J·m −2·s −1). Used in astronomy to determine the magnitude and spectral class of a star. Also acts as a generalization of heat flux, which is equal to the radiative flux when restricted to the electromagnetic spectrum.

One way to better understand the concept of flux in electromagnetism is by comparing it to a butterfly net. The amount of air moving through the net at any given instant in time is the flux. If the wind speed is high, then the flux through the net is large. If the net is made bigger hp gas kushaiguda phone number, then the flux is larger even though the wind speed is the same. For the most air to move through the net, the opening of the net must be facing the direction the wind is blowing. If the net is parallel to the wind, then no wind will be moving through the net. The simplest way to think of flux is how much air goes through the net, where the air is a velocity field and the net is the boundary of an imaginary surface.

An electric charge, such as a single electron in space, has a magnitude defined in coulombs. Such a charge has an electric field surrounding it. In pictorial form, an electric field is shown as a dot radiating lines of flux gas gangrene called Gauss lines. [13] Electric Flux Density is the amount of electric flux, the number of lines, passing through a given area. Units are Gauss/square meter. [14]

If one considers the flux of the electric field vector, E, for a tube near a point charge in the field the charge but not containing it with sides formed by lines tangent to the field, the flux for the sides is zero and there is an equal and opposite flux at both ends of the tube. This is a consequence of Gauss’s Law applied to an inverse square field. The flux for any cross-sectional surface of the tube will be the same. The total flux for any surface surrounding a charge q is q/ε 0. [17]

In free space the electric displacement is given by the constitutive relation D = ε 0 E, so for any bounding surface the D-field flux equals the charge Q A within it. Here the expression flux of indicates a mathematical operation and, as can be seen, the result is not necessarily a flow, since nothing actually flows along electric field lines.

The time-rate of change of the npower electricity bill magnetic flux through a loop of wire is minus the electromotive force created in that wire. The direction is such that if current is allowed to pass through the wire, the electromotive force will cause a current which opposes the change in magnetic field by itself producing a magnetic field opposite to the change. This is the basis for inductors and many electric generators.