Flux

Flux

Suppose that as in  you aim a wide air stream of uniform velocity small square loop of area A Let  represent the volume ate (volume per unit time) at which air flows through the loop This rate depends on the angle between  and the plane of the loop If  is perpendicular to the plane the rate  is equal to  If v is parallel to the plane of the loop no air moves through the loop so  zero For an intermediate angle 8 the rate depends on the component of v that  normal to the plane  Since that component is cos 8 the rate of volume flow through the loop. His rate of flow through an area is an example of a flux-a volume flux in thigh situation before we discuss a flux that is involved in electrostatics we need to rewrite in terms of vectors A uniform air stream of velocity V is perpendicular to the plane of a square loop of area A  (b) The Air flow component of perpendicular to the plane of the loop is cos 8 where 8 is the angle between V and a normal to the plane (e) The area vector X is perpendicular to the plane of the loop and makes an angle 8 with V (d) the velocity field intercepted by the area of the loop.

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To do this we first define an area vector A as being a vector whose magnitude is equal to an area (here the area of the loop) and whose direction is normal to the plane of the area We then rewrite as the scalar (or dot) product of the velocity vector  of the air stream and the area vector A of the loop

<P= \’A cos ()= I” – A.

where  is the angle between I and A The word flux comes from the Latin word meaning to flew That meaning makes sense if we talk about the flow of air volume through the loop However  can be regarded in a more abstract way To see it note that we can assign a velocity vector to each point in the air stream passing through the loop The composite of all those vectors is a velocity field so we can interpret  giving the flux other velocity field through the loop with this interpretation flux no longer means the actual flow of something through an area-rather it means the product of an area and the field across that area.

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