In a uniform electric field , a perfectly conducting particle having radius has a dipole moment…

In a uniform electric field f4106fdd 27df 4325 a6ee 962d1aafdbbe, a perfectly conducting particle having radius 80e2874b 71cc 4f64 abcc b73672f3d8da has a dipole moment abb0ea34 9e04 45f2 99d1 b8b37a9e3242 Provided that 80e2874b 71cc 4f64 abcc b73672f3d8da is short compared to distances over which the field varies, this gives a good approximation to b5fddb84 c04c 46b4 a6be ee02e35599a5, even where the field is not uniform. Such a particle is shown at the location 0931b6d3 90aa 47cc ac61 cdb856ad17fc in Fig. P11.8.1, where it is subject to the field produced by a periodic potential 8eb4d63c 6b43 45f2 a6ee fc1a3fae857d cos(0b6e2a16 a04d 4dc9 bd75 00dc588ecb08) imposed in the plane 45ffd496 a8cb 486b b305 ccf6e419e851

(a) Show that the potential imposed in the region 0a6a95c4 ead7 4119 ab37 a08414abc6d5 is 3d1d8ba6 9a7f 46b2 93e3 3f1a791bf59b cos(0b6e2a16 a04d 4dc9 bd75 00dc588ecb08) exp (591d0c9b 887c 4ff3 95a1 fec320f56223). (b) Show that, provided that the particle has no net charge, the force on the particle is

e4200a70 387c 4d63 b536 200183e96e38

Fig. P11.8.1

76e86ab1 e53e 4ca9 922d 79b39435415b

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