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lecture8 notes

# lecture8 notes - 8.022 Lecture Notes Class 8 What is the...

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8.022 Lecture Notes Class 8 - 09/19/2006 What is the E-Field on the axis of a circular loop of a uniformly charged thin wire with total charge q ? dE z = dE cos α = dE a 2 z + z 2 E ( z ) = 1 dq r 4 π 0 C r 3 1 ± 2 π q (cos θ ˆ i +sin θ ˆ j + zk ˆ ) = rdθ 4 π 0 0 2 πa ( a 2 + z 2 ) 3 / 2 qz k ˆ = 4 π 0 z 2 ( a 2 + z 2 ) 1 / 2 q 1 = 4 π 0 z ( a 2 + z 2 ) 1 / 2 ·

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± ± 2 Field Lines Lines start and end on charges Number of lines proportional to charge Line density pro- portional to Feld strength 1 in 3D space r 2 Never cross Point Charge at Origin E da = q r ˆ ( r 2 sin θdθdφr ˆ) where da = r ˆ( r 2 sin θdθdφ ) · 4 π 0 r 2 Sphere q = 4 π 0 r ˆ r ˆ sin θdθdφ · = q 0 E da = q · ± 0 E = Σ i E i
± 3 E da = Σ i ± E i · da = Σ i q i = 1 Q enclosed · ± 0 ± 0 Eda = Edτ V · S 1 Q enclosed = ”” ± 0 1 ± ρdτ = ± 0 V V · = E ± ρ 0 · Gaussian Surfaces and Symmetry Spherical

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lecture8 notes - 8.022 Lecture Notes Class 8 What is the...

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