Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• A pocket compass with a magnetized iron needle is at rest in the earth’s magnetic field, B ≈ 10−4 T. (a) Given that the mass of the needle is 0.2 grams, estimate its magnetic moment. Assume that each atom in the needle has a magnetic moment of one Bohr magneton and that the moments of all the atoms are fully aligned, (b) Find the ratio of the probability that the needle is pointing along the earth’s field to that of its pointing in the opposite direction at room temperature. [It is legitimate to use the Boltzmann relation in this classical situation.]
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