Chapter 22 lecture - Chapter 22 Electric Flux E and Gauss's...

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Chapter 22 Electric Flux, Φ E , and Gauss’s Law Special Note: January 17, 2006 was the 300 th Birthday of Benjamin Franklin– his letters to the Royal Society around 1750 laid the foundation for understanding electric charge and protecting buildings from lightning damage.
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Electric Field Lines (Faraday’s Lines of Force) (helpful visualizer of ) E Electric Field lines are drawn such that: 1. at any point is tangent to the line 2. Lines begin on + charge (or ∞), end on - (or ∞) 1. E is large where the lines are closely spaced E Reminder from last lecture…. Let’s make #3 more quantitative……..
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Point #3 improved (better) (E = # of lines, N, per area, A , perpendicular to E) = A N E BUT……what if E is varying in magnitude and/or direction over A?? Solution: we need to shrink A down to an infinitesimal, dA
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Point #3 improved (best) = = dA dN E E Shrink A to an infinitesimal dA and consider the infinitesimal number of lines dN poking through it. The ratio is the E field at that point: This is a dumb way to define our most fundamental concept of E!! Turn it around to define N in a fundamental fashion……. = EdA dN How do we get dA at a selected point on some arbitrary surface???
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The outward surface normal The orientation of a little “swatch” of surface is specified by it’s vector normal (perpendicular) to the surface of magnitude dA Equivalently, we can use the unit vector normal to the surface, n ˆ dA dA dA Note that dA = dAcosφ and is the component of dA perpendicular to E We can also define E = Ecosφ to be the component of E along dA or n ˆ
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Defining the FLUX, Φ E , of the Electric Field = = = = N A d E dA E EdA EdA dN A through E of flux A area total over the integrate surface, finite any for cos ϕ DEMO the FLUX!
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