Got it? (By the way, the terms “source” and “sink” are sometimes used to describe fields). So positive flux = leaving, negative = entering. Negative flux is like water entering a sink it is a sink of flux. Positive flux means flux is leaving the hose the hose is a source of flux. This decision is arbitrary, but by convention (aka your math teacher will penalize you if you don’t agree), positive flux leaves a closed surface, and negative flux enters a closed surface. One last detail – we need to decide on a positive and negative direction for flux. What matters? The strength of the waterfall, the size of the bucket and the orientation of the bucket. This is simple stuff so far, right? If you forget, just think about capturing water from a waterfall. When we figure out our total flux, we need to see how much field is passing through our entire surface. In the same field, a bigger bucket will capture more flux than a smaller one. Total flux also depends on the size of our surface. You wouldn’t capture much water (ignoring splashing) and may get a few funny looks. It would be like holding a bucket sideways under a waterfall. As the surface tilts away from the field, the flux decreases as less and less flux crosses the surface.Įventually, we get zero flux when the source and boundary are parallel - the flux is passing over the boundary, but not crossing through it. When our surface completely faces the field it captures maximum flux, like a sail facing directly into the wind. Total flux also depends on the orientation of the field and the surface. Doubling the source (doubling the “banana-ness” of each banana), will double the flux passing through a surface. The source of flux has a huge impact on the total flux. (There is a separate idea of "flux density" (flux/volume) called divergence, but that’s a separate article.) Flux is the total force you feel, the total number of bananas you see flying by your surface. Measurement: Flux is a total, and is not “per unit area” or “per unit volume”. If your field does change, then you need to pick a point in time to measure the flux. If your field doesn’t change over time, then all is well. Freeze time and ask “Right now, at this moment, how much stuff is passing through my surface?”. Timing: We measure flux at a single point in time. We’re considering the flux passing through the region the circle defines. Notice that the boundary may not exist - the top of a bucket traces out a circle, but the hole isn’t actually there. The boundary could be a sphere, a plane, even the top of a bucket. Surface: This is the boundary the flux is crossing through or acting on. Flux doesn’t have to be a physical object - you can measure the “pulling force” exerted by a field. Vector Field: This is the source of the flux: the thing shooting out bananas, or exerting some force (like gravity or electromagnetism). Keep a few ideas in mind when considering flux: The strength of the field is important – would you rather have a handful of \$5 or \$20 bills “flux” into your bank account? Would you rather have a big or little banana come your way? No need to answer that one. The source of the flux (strength of the field, and which way it is spitting out bananas flux).The surface you are considering (shape, size and orientation).bananas) passing through a surface, we need to know I find bananas more memorable, so we’ll be using those. Math books will use abstract concepts like electric fields, which is pretty hard to visualize. This “something” can be water, wind, electric field, bananas, pretty much anything you can imagine. Think of flux as the amount of something crossing a surface. And who doesn’t want that? Physical Intuition Your vector calculus math life will be so much better once you understand flux. The total flux depends on strength of the field, the size of the surface it passes through, and their orientation.Flux is the amount of “something” (electric field, bananas, whatever you want) passing through a surface.However, it took a lot of effort to truly understand that: The formulas become “obvious” dare I say. Once you understand flux intuitively, you don’t need to memorize equations.
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