4-space Curl in Vector Calculus - Gauge-institute.org

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Gauge Institute Journal, Volume 9, No. 3, August 2013 H. Vic Dannon 2. The Non-Vanishing Magnetic Induction on the Electron Clearly, Hence, A 1θ =− 1x sinθ + 1y cos θ = y =− 1x + 1 b 2 aB 2b 1 θ y x b 2 2 =− y1 + x1 aB aB 2 2 2b x 2b y 10
Gauge Institute Journal, Volume 9, No. 3, August 2013 H. Vic Dannon Therefore, 2 aB = x 2 ⎢ ⎥ 2b ⎡ y ⎤ − ⎢ ⎥ . 0 ⎢⎣ ⎥⎦ B =∇× A ⎡−y ⎤ 2 aB = ∇× x 2 2b 0 ⎢⎣ ⎥⎦ 1 1 1 2 aB 2 2b −y x y z = ∂ ∂ ∂ x y z x 0 2 aB = 0 2 ⎢ ⎥ 2b ⎡0 ⎤ ⎢ ⎥ 2 ⎢⎣ ⎥⎦ = 2 aB b 2 1 . z That is, the Magnetic Induction at the electron, at r = b, is the non-zero 2 aB1 2 . B = This field is not negligible! For instance, if the electron orbit has radius b = 2a, then the Magnetic Induction is B B = , which is far from negligible. 1 4 z b z 11
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