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James A. Van Allen lab journal, September 1959-January 1961
Page 187
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Net Loop E.M.F. (ABCD) = b (E sub 0) [(sine (w)(t)) - (sine (((w)(t)) - ((2pi(a))/(lambda))))] =b (E sub [0? v?]) [(sine ((w)(t)))-((sine (w)(t))(cosine ((2pi(a))/(lambda)))+((cosine ((w)(t)))(sine ((2pi(a))/(lambda))))] [red ink circled below here:] ~= ((2pi(E sub 0)A)/(lambda)) ([cosine?] (w)(t)) [red ink circled above here] where A = ab = area of loop. (B): phi (through loop) = By A =((B sub 0) A) (sine (((w)(t)) - ((2pi/lambda)([a?]/2)))) ~= ((B sub 0) A) (sine (w)(t)). w=2pi(f) =((2pi(C))/(lambda)) Loop E.M.F. = (([2?]phi)/([2?]t)) = (((B sub 0)(A)(w))(cosine ((w)(t)))) [red ink circled below here:] = ((2pi(C)(B sub 0)A)/(lambda)) (cosine ((w)(t))) = ((2pi(E sub 0)A)/(lambda)) (cosine ((w)(t))). [red ink circled above here]
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Net Loop E.M.F. (ABCD) = b (E sub 0) [(sine (w)(t)) - (sine (((w)(t)) - ((2pi(a))/(lambda))))] =b (E sub [0? v?]) [(sine ((w)(t)))-((sine (w)(t))(cosine ((2pi(a))/(lambda)))+((cosine ((w)(t)))(sine ((2pi(a))/(lambda))))] [red ink circled below here:] ~= ((2pi(E sub 0)A)/(lambda)) ([cosine?] (w)(t)) [red ink circled above here] where A = ab = area of loop. (B): phi (through loop) = By A =((B sub 0) A) (sine (((w)(t)) - ((2pi/lambda)([a?]/2)))) ~= ((B sub 0) A) (sine (w)(t)). w=2pi(f) =((2pi(C))/(lambda)) Loop E.M.F. = (([2?]phi)/([2?]t)) = (((B sub 0)(A)(w))(cosine ((w)(t)))) [red ink circled below here:] = ((2pi(C)(B sub 0)A)/(lambda)) (cosine ((w)(t))) = ((2pi(E sub 0)A)/(lambda)) (cosine ((w)(t))). [red ink circled above here]
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