16th-ipho85 - Problems and solutions of the 16th IPhO...

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Unformatted text preview: Problems and solutions of the 16th IPhO * Portoroˇ z, Slovenia, (Former Yugoslavia), 1985 Contents 1 Problems 2 1.1 Theoretical competition . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Experimental competition . . . . . . . . . . . . . . . . . . . . . . 5 2 Solutions 9 2.1 Theoretical competition . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Experimental competition . . . . . . . . . . . . . . . . . . . . . . 16 1 Problems 1.1 Theoretical competition Problem 1 A young radio amateur maintains a radio link with two girls living in two towns. He positions an aerial array such that when the girl living in town A receives a maximum signal, the girl living in town B receives no signal and vice versa. The array is built from two vertical rod aerials transmitting with equal intensities uniformly in all directions in the horizontal plane. * Edited by B. Golli, Faculty of Education, University of Ljubljana, and J. Stefan Insti- tute, Ljubljana, Slovenia, e-mail: [email protected] 1 a) Find the parameters of the array, i. e. the distance between the rods, its orientation and the phase shift between the electrical signals sup- plied to the rods, such that the distance between the rods is mini- mum. b) Find the numerical solution if the boy has a radio station transmit- ting at 27 MHz and builds up the aerial array at Portoroˇ z. Using the map he has found that the angles between the north and the direc- tion of A (Koper) and of B (small town of Buje in Istria) are 72 ◦ and 157 ◦ , respectively. Problem 2 In a long bar having the shape of a rectangular parallelepiped with sides a , b , and c ( a b c ), made from the semiconductor InSb flows a current I parallel to the edge a . The bar is in an external magnetic field B which is parallel to the edge c . The magnetic field produced by the current I can be neglected. The current carriers are electrons. The average velocity of electrons in a semiconductor in the presence of an electric field only is v = μE , where μ is called mobility. If the magnetic field is also present, the electric field is no longer parallel to the current. This phenomenon is known as the Hall effect. a) Determine what the magnitude and the direction of the electric field in the bar is, to yield the current described above. b) Calculate the difference of the electric potential between the oppo- site points on the surfaces of the bar in the direction of the edge b . c) Find the analytic expression for the DC component of the electric potential difference in case b) if the current and the magnetic field are alternating (AC); I = I sin ωt and B = B sin (ωt + δ) . d) Design and explain an electric circuit which would make possible, by exploiting the result c), to measure the power consumption of an electric apparatus connected with the AC network....
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This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.

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16th-ipho85 - Problems and solutions of the 16th IPhO...

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