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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
semicircular 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 cathoderay 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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 Fall '10
 ProfessorSomi

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