Download Problems and solutions on electromagnetism: major American by Yung-Kuo Lim PDF

By Yung-Kuo Lim

The cloth for those volumes has been chosen from the earlier two decades' exam questions for graduate scholars at collage of California at Berkeley, Columbia collage, the college of Chicago, MIT, kingdom college of recent York at Buffalo, Princeton collage and college of Wisconsin.

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Extra info for Problems and solutions on electromagnetism: major American University Ph.D. qualifying questions and solutions

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14. The total charge on the conductor itself is zero. However, there is a point charge +Qb at the center of one cavity and +qc at the center of the other. A large distance r away is another charge +Qd. What forces act on each of the four objects A,qb,q,, and Qd? Which answers, if any, are only approximate and depend on r being very large. Comment on the uniformities of the charge distributions on the cavity walls and on A if r ie not large. ( Wisconsin) I I - r - , I I I I a qd q C Fig. 14 Solution: Charges outside a cavity have no influence on the field inside because of the electrostatic shielding by the conductor.

Wisconsin) Solution: Since the current is the electric field is and the potential is Hence the current between the spheres is given by I = 4 r K V’/ ln(b/a) . 20 Problcmr EI Solulionr o n E/cciromi#neiirm 1019 An isolated soap bubble of radius 1 cm is at a potential of 100 volts. If it collapses to a drop of radius 1 mm, what is the change of its electrostatic energy? ( Wisconsin) Solution: If the soap bubble carries a charge Q, its potential is For r = rl = 1 cm, V = V1 = 100 V,we have Q = 4ueorlV1.

DS=a 6 If the potential difference between the two conductors is V, we have V = I R = +R, whence Numerically the capacitance between the conductors is 1046 Consider a long cylindrical coaxial capacitor with an inner conductor of radius a, an outer conductor of radius b, and a dielectric with a dielectric constant K(r), varying with cylindrical radius r . The capacitor is charged to voltage V. Calculate the radial dependence of K(r) such that the energy density in the capacitor is constant (under this condition the dielectric has no internal stresses).

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