DUE ON NOVEMBER 17, 2005
6 Figure 28-29 shows the path of a particle through six regions of uniform magnetic field, where the path is either a half-circle or a quarter-circle. Upon leaving the last region, the particle travels between two charged, parallel plates and is deflected toward the plate of higher potential. What is the direction of the magnetic field in each of the six regions?
•••10 At time t1, an electron is sent along the positive direction of an x axis, through both an electric field and a magnetic field , with directed parallel to the y axis. Figure 28-34 gives the y component Fnet,y of the net force on the electron due to the two fields, as a function of the electron's speed v at time t1. The x and z components of the net force are zero at t1. Assuming Bx = 0, find (a) the magnitude E and (b) in unit-vector notation.
••13 In Figure 28-36, a conducting rectangular solid of dimensions dx = 5.00 m, dy = 3.00 m, and dz = 2.00 m moves at constant velocity through a uniform magnetic field . What are the resulting (a) electric field within the solid, in unit-vector notation, and (b) potential difference across the solid?
••25 A certain commercial mass spectrometer (see Sample Problem 28-3) is used to separate uranium ions of mass 3.92 × 10–25 kg and charge 3.20 × 10–19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.00 m. After traveling through 180° and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 100 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.00 h.
64 A proton travels through uniform magnetic and electric fields. The magnetic field is . At one instant the velocity of the proton is . At that instant and in unit-vector notation, what is the net force acting on the proton if the electric field is (a) , (b) , and (c) 4.00î V/m?
74 In Figure 27-65, R1 = 20.0 Ω, R2 = 10.0 Ω, and the ideal battery has emf = 120 V. What is the current at point a if we close (a) only switch S1, (b) only switches S1 and S2, and (c) all three switches?
•3 An electron that has velocity moves through the uniform magnetic field . (a) Find the force on the electron. (b) Repeat your calculation for a proton having the same velocity.
••9 An ion source is producing 6Li ions, which have charge +e and mass 9.99 × 10–27 kg. The ions are accelerated by a potential difference of 10 kV and pass horizontally into a region in which there is a uniform vertical magnetic field of magnitude B = 1.2 T. Calculate the strength of the smallest electric field, to be set up over the same region, that will allow the 6Li ions to pass through undeflected.
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