1) (Application ) Almost all motors are made by winding many turns of wire around pieces of iron , arranged so that some of the pieces of iron can turn inside the other pieces . Given that electric motors work on the principle of one magnetic dipole causing another to rotate : why aren't motors made of simple coils of wire ? 2) (Application ) In each of the four pictures below electrons flow inside a tube that is evacuated (i.e., there is no air inside ). The solid curve shows the electrons 'paths and the arrows show their direction There is an electric field in each tube that is created by electric charges placed at each end , as shown A uniform magnetic field B is also present inside the tube , created by some external source . The magnetic field points either directly into the page or directly out of the page . For each diagram , decide if the electrons s are slowing down or speeding up and decide if the magnetic field points into the page or out of the page . You may neglect gravity in this problem . Clearly explain your reasoning (I) (II ) (III) (IV) path bath path path 3) (Application ) In the picture to right of a mass spectrometer a charged ion (charge q) is accelerated by an Oby R electric field and then enters a region where the magnetic field . B. is uniform and points out of the page as shown . The ion follows the circular arc shown and is detected a distance 2R from where it entered a) Explain roughly why the ion curves to the left, why the a horizontal row of path is circular , and why its speed does not change as it particle detectors curves . (Hint : what charge must the ion have ?) b) An object , like this ion, moving at a constant speed : v, along an arc of constant radius , R, must experience a centripetal force of magnitude F = mv /R pointing toward the center of the circle Use this formula for the acceleration and the formula for the magnetic force on a moving charge to write R as a function of v. B. and m. If there are a whole row of detectors , and all ions enter with the same speed , which ones will detect the particles with the largest masses ? (Application ) In the mass spectrometer discussed above all the ions enter with the same speed This means that there must be a piece of equipment that will pick out one speed from all the possible ion speeds and this speed should not depend on the mass . m, or charge : q: the of the ion . Such a piece of equipment is shown to the right . All ions entering with the right speed move straight through along the path represented by the solid line . Ions with different speeds have curved paths like the dotted lines and thus do not emerge on the other side . The key to getting this to happen is to have both a uniform electric field and a uniform magnetic field in the tube . Decide the directions of these fields and explain why ions of only one speed make it through , regardless of the mass or the charge of the ion