What is meant by paramagnetism and diamagnetism? Give a short qualitative explan

Question

What is meant by paramagnetism and diamagnetism? Give a short qualitative explanation for each phenomenon at the microsopic level. What is Faraday's law? Briefly describe an experiment that led Faraday to his conclusion? See the figure on the back side of this page. A Bainbridge mass spectrometer is used to separate a beam of ions into its various mass components. It consists of two regions of space separated by a slit, the first with a combination of an electric field E and a magnetic field B, the second with only a magnetic field B. In what direction must B point if we want positively charged ions to have the trajectory shown in the figure? What about E? Notice that E and B must combine to give a straight-line trajectory in the first part of the filter. If the magnitude of the E field is 100 V/m and the B field is 0.2 T, what is the velocity of the ions that make it through the slit? At what distance d from the slit should we put a particle detector to collect singly-charged 3He ions? What about^4He? Use non-relativistic mechanics. Useful information: m(^3He) = 3 amu; m(^4He)= 4 amu; 1 amu = 1.66 times 10^-27kg; unit charge (e) = 1.6 times 10^-19C What magnetic field B corresponds to a vector potential A = phi^2 z in cylindrical coordinates? What current density J would generate such a field? Assume this is all done in vacuum. Why can the field B = k s (k is a constant; again in cylindrical coordinates) not be a real magnetic field? A current flows down a long straight wire of radius a. If the wire is made of linear material with susceptibility Xm, and the current is distributed uniformly, what is the magnetic field B a distance s from the axis? Solve for both cases: s a. Find all the bound currents.

Explanation / Answer

Part 1: All atoms can be thought of as magnetic dipoles (having north pole and south pole) which behave in different ways when placed in an external magnetic field. These atomic dipoles are randomly oriented inside the material. Sometimes, the external magnetic field alligns all the atomic dipoles in its direction. This tendency of the material to increase its magnetization by alligning the atomic dipoles with the direction of the applied field is called paramagnetism.

On the other hand, some materials allign their atomic dipoles in the opposite direction of the applied magnetic field and decrease their magnetization due to Lenz's law. This tendency of the materials is called diamagnetism.

Part 2: Faraday's law states that any change in the magnetic flux linked with a coil will cause an emf to be induced in the coil.

A coil of wire is connected to a gavanometer. A bar magnet is taken near the coil, it is seen that an induced current flows through the galvanometer. When the magnet is taken away from the coil, an induced current again flows through the galvanometer but in the opposite direction. The experiment is repeated. So, a to and fro motion of the bar magnet changes the magnetic flux linked with the coil which results in a production of induced emf, hence current.

Part 3: (a) The magnetic field, B must point inside the plane of the computer screen. This will make the particle move towards right ( using the equation F=q(vXB). In order to keep the particle in a straight line, the electric field, E must point from right to left.

Part 3: (b) Velocity of particle,

v= E/B

=100/0.2 m/s

= 500 m/s

Part 3 (c): Distance from the slit to the screen = Diameter of the semicircle.

= 2Mv/Be

Put the values of mass(M) and charge (e) from the 'useful information'. Put v as 500 m/s and B as 0.2T and get the answer. Repeat the same for 4He, just by changing e by 2e, as the ion is doubly charged.

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