prob6 - M50 H2. {peoecermt (9 1. Fig. 1 shows a mass...

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Unformatted text preview: M50 H2. {peoecermt (9 1. Fig. 1 shows a mass spectrometer, in which ions of mass m and charge q are accelerated through a potential difference of V before describing semi-circular paths in a region with constant magnetic field B. They strike a detector a lateral distance x from where they enter the field. (a) Obtain an expression for x in terms of V, B, m and q. (b) If the spectrometer is used to analyse a gas sample containing singly- ionized C0 and 02 ions with V = 1000 V and B = 0.2 T, what values of x will be observed? (C and 0 have masses of 12 and 16 amu, where l amu = 1.67 x 10'27 kg). 2. Electrons in a magnetic field of 0.005 T execute a helical path of radius 2 cm, with a pitch (distance between turns) of 6 cm. (a) What is the speed of the electrons? (b) What magnitude and direction of electric field would be required to cause the electrons to move with constant velocity? 3. A cathode-ray tube uses a potential difference of 30 kV to accelerate electrons along the x axis. The electrons then pass through a uniform magnetic field B of strength 0.0065 T in the z direction, which extends for a distance of 3.5 cm along the x axis. After being deflected, the electrons continue in a straight line until they hit a screen at a distance of 22 cm (measured along x) beyond the region of B. (a) What is the speed of the electrons when they enter and leave the magnetic field? (b) What angle of deflection do the electrons undergo in the region of the magnetic field? (c) What is the total deflection along y when the electrons hit the screen? 4. A 50 g copper rod rests on two horizontal rails 1 m apart, and carries a current of 10 A from one rail to the other.(See Fig. 2). The coefficient of static friction between the rod and the rails is 0.60. (a) If there is a vertical magnetic field, how large must it be to cause the rod to SE ? (b) What is the smallest magnetic field which will cause the rod to slip, and what direction must it be in? 5. The current i in the circuit of Fig. 3, which lies in the xy plane, is i = 20 A. The circuit is in a uniform magnetic field of 0.5 T which makes an angle of 40° with the z direction. (a) What force acts on the circuit? (b) What magnitude of torque acts on it? 6. A uniform square loop with mass M and current i lies in the xy plane as shown in Fig. 4 and is supported by a light, frictionless axle through its centre along 3!. There is a uniform magnetic field B in the z direction. Show that if the loop is displaced through a small angle 6 and then released it will perform simple harmonic oscillation about 9 = 0, and find the period. 7. An electron moves with a velocity of (3 i + 4i)x105 mfs in a combination of an electric field, and a magnetic field of 0.005 T in the z direction. The force on the electron is measured to be 51:1016 N in the x direction. What is the magnitude and direction of the electric field? Fig. 1 2i 100m 10cm Fig. 3 20cm our Ie. Fig. 4 ...
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prob6 - M50 H2. {peoecermt (9 1. Fig. 1 shows a mass...

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