ˆB F qv B q v v B qv B qv n = × = + × = × = mv mv qB v F qv B r r m r
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r r r r r r r r FB = qv × B = q ( vP + v⊥ ) × B = qv⊥ × B = qv⊥B nˆ B vP v θ FB = qvsenθ B v⊥ mv⊥2 FB = r B FB r Por otro lado ∴ qBr = mv⊥2 → qv⊥ B = r → qB v⊥ = m r qBr = mvsenθ K = ∆U 2U senθ m o sea, → 1 2 2U mv = U → v = 2 m 2mU senθ r= qB Como v⊥ = 2π r T → T= 2π r m = 2π ⋅ v⊥ qB Además, en el tiempo T la partícula “avanza” p con rapidez vP = v cosθ o sea, p = v cos θ ⋅ T = 2U 2π m 2π cos θ ⋅ = 2mU cos θ ⋅ m qB qB Numéricamente 2π ⋅ 9,11 ⋅10−31 −6 T= = 8.9 × 10 [ s] −19 −6 1.6 ⋅ 10 ⋅ 400 ⋅10 p = 2 ⋅ 9.11⋅ 10−31 ⋅ 20 ⋅1.6 ⋅10−19 cos85 = 6.6 ⋅ 10−3 [ m ] 2π = − 19 −6 1.6 ⋅10 ⋅ 400 ⋅10 2 ⋅ 9.11 ⋅10−31 ⋅ 20 ⋅1.6 ⋅10−19 sen85 −2 r= = 3.8 ⋅ 10 [ m] −19 −6 1.6 ⋅ 10 ⋅ 400 ⋅10
