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A Dipole near a Point Charge.
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In Section 26.3, Knight claimed that a charged object exerts a net attractive force on an electric dipole. Let's investigate this. Consider a permanent elec- tric dipole consisting of charges +q and -q separated by a fixed vector distance Ŝ, with this vector directed from – q to +9. The charge +Q is a displacement Ť from the center of the dipole, and the dipole is oriented so that ŝ and † are antiparallel, which is the lowest-energy configuration. (This means that the negative end of the dipole points toward Q. For convenience, draw the charges on a horizontal line, with the charges in order, from left to right, as q,-9,+Q.) We'll assume, as is usually the case in practice, that s«r. a) Write an expression for the magnitude of the net force exerted on the dipole by the charge +Q. (Answer: Fnet = ). Of course, you 4 л во (r - 3/2) (r + s/2) need a detailed picture here!) b) Is this force on the dipole toward +Q or away from +Q? Explain. c) Use the binomial expansion (1 + x) -" - 1 - nx + ... if x« 1 to show that your expression in part (a) for the magnitude of the force can be written as Qqs 2160p d) How can an electric force have an inverse-cube dependence? Doesn't Coulomb's law say that the electric force depends on the inverse square of the distance? Explain. 1 1 = Fnet