# Th2 Solution - 36 th International Physics Olympiad...

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Unformatted text preview: 36 th International Physics Olympiad. Salamanca (España) 2005 Solution Th 2 Page 1 of 4 R.S.E.F. Th 2 ABSOLUTE MEASUREMENTS OF ELECTRICAL QUANTITIES SOLUTION 1. After some time t , the normal to the coil plane makes an angle ω t with the magnetic field i B B r r = . Then, the magnetic flux through the coil is S B N r r ⋅ = φ where the vector surface S r is given by ( ) j t i t a S r r r ω ω π sin cos 2 + = Therefore t B a N ω π φ cos 2 = The induced electromotive force is dt d φ ε − = ⇒ t B a N ω ω π ε sin 2 = The instantaneous power is = P ε 2 /R , therefore ( ) R B a N P 2 2 2 ω π = where we used 2 1 sin 1 sin 2 2 = >= < ∫ T dt t T t ω ω 2. The total field at the center the coil at the instant t is i t B B B r r r + = where i B r is the magnetic field due to the induced current ( ) j t i t B B i i r r r ω ω sin cos + = with a I N B i 2 µ = and I = ε / R Therefore t R B a N B i ω ω π µ sin 2 2 = The mean values of its components are R B a N t R B a N...
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Th2 Solution - 36 th International Physics Olympiad...

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