Exercise 9 - Magnetism-The Lorentz Force

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Exercise 9 - Magnetism-The Lorentz Force
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Four particles follow the paths shown in Fig. 32-33 below as they pass through the magnetic field there. What can one conclude
about the charge of each particle?
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A 1.22-keV electron is circulating in a plane at right angles to a uniform magnetic field. The orbit radius is 24.7 cm. Calculate
(a) the speed of the electron, (b) the magnetic field, (c) the frequency of revolution, and (d) the period of motion.
A cosmic ray proton (mp = 1.67 x 10-27 kg) strikes the Earth near the equator with a vertical velocity of 2.8 x 10 7 m/s. Assume
that the horizontal component of the Earth's magnetic field at the equator is 30 mT. Calculate the ratio of the magnetic force on
the proton to the gravitational force on it.
A proton traveling at 23.0? with respect to a magnetic field of strength 2.63 mT experiences a magnetic force of 6.48 x 10-17 N.
Calculate (a) the speed and (b) the kinetic energy in eV of the proton. (mp = 1.67 x 10-27 kg)
An electric field of 1.5 kV/m and a magnetic field of 0.44 T act on a moving electron to produce no force. (a) Calculate the
minimum electron speed v. (b) Draw the vectors E, B, and v, indicating their relative orientations.
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A metal wire of mass m slides without friction on two horizontal rails spaced a distance d apart, as shown in Fig. 32-36 below.
The track lies in a vertical uniform magnetic field B. A constant current i flows from the generator G along one rail, across the
wire, and back down the other rail. Find the velocity (speed and direction) of the wire as a function of time, assuming it to be at
rest at t=0.
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Figure 32-40 below shows an arrangement used to measure the masses of ions. An ion of mass m and charge
essentially at rest in source S, a chamber in which a gas discharge is taking place. The ion is accelerated by a poten
DV and allowed to enter a magnetic field B. In the field it moves in a semi-circle (as shown in the figure), striking
plate at distance x from the entry slit. Show that the ion mass m is given by m = (B2qx2)/(8DV).
b.
Two types of singly ionized atoms having the same charge q and mass differing by a small amount Dm are
spectrometer described in the previous problem and shown in Fig. 32-40 above. (a) Calculate the difference in mass
q, m (of either), B, and the distance Dx between the spots on the photographic plate. (b) Calculate Dx for a bea
chlorine atoms of masses 35.0 u and 37.0 u if DV = 7.33 kV and B = 520 mT. (An atomic mass unit is given by u
kg.)
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A length L of wire carries a current i. Show that if the wire is formed into a circular coil, the maximum torque in a given
magnetic field B is developed when the coil has one turn only and the maximum torque has the magnitude t = L2iB/(4p).
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