IPhO 2017 Problem 5

Physics

Problem

Experiment E2 English (Official) page 1 of 11 Experiment E2 English (Official) x y y 0 z z page 2 of 11 Experiment E2 English (Official) M χ χ Q μ A page 3 of 11 Experiment E2 English (Official) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. page 4 of 11 Experiment E2 English (Official) 11. − 12. 13. 14. 15. 1. 2. 3. 4. R L gM 3 ρ d d d d T −6 μ0 × −23 2 2 kB × 2 g page 5 of 11 Experiment E2 English (Official) M m M m M = πR2L R L M M x B x ≤ μ m B (x) = 0 I 2πxPL x x page 6 of 11 Experiment E2 English (Official) B 0 B x ≤ x ≤ x p M 1. 2. 3. x R 4. 5. 6. x OFFSET 7. x x page 7 of 11 Experiment E2 English (Official) χ y 0 y 0 F M(y 0) χ y 0 μ = (1 + χ)μ 0 μ F M (y 0 ) = − μ 0 M 2 2χV r R a5 4 f ( y a 0 ) F (y ) M 0 V M r a a = R + g /2 M g g f(u) M M 4u(3−u2 )(1−u2 ) f(u) = (1+u2) 5 y 0 χ page 8 of 11 Experiment E2 English (Official) χ y 0 χ z U = 1 k z2 M z 2 k z z k M χ z k = −C μ χM2V z 1 0 r μ V C 2 0 r 1 l A χ page 9 of 11 Experiment E2 English (Official) −t/τ μ z(t) = Ae sin(ωt) A A ω = 2πf t −t/τ τ Q = ωτ/2 Q Q Q τ 2 ρr2 l τ = ln(0.607 × ) 3 μ A r ρ r l μ A τ τ τ μ A 2 0.5 ) ‾4‾k‾ B ‾T‾ω‾ a = n √ QmR k B T m R τ page 10 of 11 Experiment E2 English (Official) a n S S l Δz S N Δz N S Q page 11 of 11

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