A wire is formed into a circle having a diameter of 10.0 ?? and placed in a uniform magnetic field of 3.00 ??. The wire carries a current of 5.00 ?. Find (a) the maximum torque on the wire and (b) the range of potential energies of the wire–field system for different orientations of the circle.

(Figure 1) shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to- mass ratio q/m. The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference AV, and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Consider a mass spectrometer with a 200.00 mT magnetic field and an 8.0000 cm spacing between the entrance and exit holes. igure + AV d Detector Part A To five significant figures, what accelerating potential difference AV is required to detect the ion O,? The masses of the atoms are shown in the table; the mass of the missing electron is less than 0.001 u and is not relevant at this level of precision. Use…

A ring of radius 8.0 cm is placed concentrically around a ring of radius 6.0 cm (see figure below). Each ring carries a current of 4.0 A.(a) What is the magnitude of the magnetic field at the center of the rings if the two currents flow in the same direction?(b) Find the magnitude of the magnetic field if the currents flow in opposite directions?(c) If the outer ring current is counterclockwise and the inner ring current is clockwise what is the direction of the net magnetic field

Two very long, parallel wires are separated by a distance of 2 m. The top wire carries a current of 16 A flowing to the left. Point x lies between the wires, 0.4 m below the top wire (see figure below).  (a) What is the strength of the magnetic field at point x due to the top wire? For part (a) and (b) you may assume no current is flowing in the bottom wire.  (b) What is the direction of the magnetic field at point x due current flowing in the top wire? (Give your answer in terms of toward the top, bottom, left side, right side, into, or out of the page.)  (c)  What current must flow through the bottom wire to have the net (total) magnetic field be zero at point x? Specify both the magnitude and the direction of the current.

An electron moves in a circular path perpendicular to a uniform magnetic field with a magnitude of 1.98 mT. If the speed of the electron is 1.40 x 107 m/s, determine the following. (a) the radius of the circular path cm (b) the time interval required to complete one revolution

53. A wire is formed into a circle having a diameter of w 10.0 cm and is placed in a uniform magnetic field of 3.00 mT. The wire carries a current of 5.00 A. Find (a) the maximum torque on the wire and (b) the of potential energies of the wire-field system for differ- range ent orientations of the circle.