1. A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 x 10-25 kg and charge 3.20 x 10-19 C from related species. The ions are accelerated through a potential difference of 101 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 0.864 m. After traveling through 180 and passing through a slit of width 0.758 mm and height 1.48 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 0.849 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 1.24 h. Detector 2. The coil in the figure carries current i = 2.39 A in the direction indicated, is parallel to an xz plane, has 6 turns and an area of 5.63 x 10-3 m2, and lies in a uniform magnetic field B = (2.21 1 - 3.58 j - 4.74 k) mT. (a) What is the magnetic potential energy of the coil- magnetic field system? (b) What is the magnetic torque (in unit-vector notation) on the coil? 3 . A wire lying along an x axis from x = 0 to x = 0.944 m carries a current of 2.58 A in the positive x direction. The wire is immersed in a nonuniform magnetic field given by B = (4.15 T/m2)x21 - (0.654 T/m2)x2j. In unit-vector notation, what is the magnetic force on the wire? 4. In the figure, point P1 is at distance R = 12.3 cm on the perpendicular bisector of a straight wire of length L = 19.3 cm carrying current / = 66.8 mA. (Note that the wire is not long.) (a) What are the magnitude of the magnetic field at P1 and pint P2 due to