Some types of bacteria contain chains of ferromagnetic particles parallel to their long axis. The chains act like small bar magnets that align these magnetotactic bacteria with the earth’s magnetic field. In one experiment to study the response of such bacteria to magnetic fields, a solenoid is constructed with copper wire 1.0 mm in diameter, evenly wound in a single layer to form a helical coil of length 40 cm and diameter 12 cm. The wire has a very thin layer of insulation, and the coil is wound so that adjacent turns are just touching. The solenoid, which generates a magnetic field, is in an enclosure that shields it from other magnetic fields. A sample of magnetotactic bacteria is placed inside the solenoid. The torque on an individual bacterium in the solenoid’s magnetic field is proportional to the magnitude of the magnetic field and to the sine of the angle between the long axis of the bacterium and the magnetic-field direction. What current is needed in the wire so that the magnetic field experienced by the bacteria has a magnitude of 150μT? (a) 0.095 A; (b) 0.12 A; (c) 0.30 A; (d) 14 A.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

How is the gravitational force related to the distance between two objects?

Karen is running forward at a speed of 9 m/s. she tosses her sweaty headband backward at a speed of 20 m/s. the speed of the headband, to the nearest whole number relative to a stationary observer watching karen