DUE ON SEPTEMBER 29, 2005
4 Figure 22-23 shows two square arrays of charged particles. The squares, which are centered on point P, are misaligned. The particles are separated by either d or d/2 along the perimeters of the squares. What are the magnitude and direction of the net electric field at P?
••15 Figure 22-36 shows an uneven arrangement of electrons (e) and protons (p) on a circular arc of radius r = 2.00 cm, with angles q1 = 30.0°, q 2 = 50.0°, q 3 = 30.0°, and q 4 = 20.0°. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the net electric field produced at the center of the arc?
••16 Figure 22-37 shows a plastic ring of radius R = 50.0 cm. Two small charged beads are on the ring: Bead 1 of charge +2.00 mC is fixed in place at the left side; bead 2 of charge +6.00 mC can be moved along the ring. The two beads produce a net electric field of magnitude E at the center of the ring. At what (a) positive and (b) negative value of angle q should bead 2 be positioned such that E = 2.00 × 105 N/C?
••20 The electric field of an electric dipole along the dipole axis is approximated by Equation 22-8 and Equation 22-9, which result from the termination of the two binomial expansions shown just before those equations. If the expansions were carried out further, what would be the next nonzero term in the expression for the dipole's electric field along the dipole axis? That is, what is Enext in the expression
•••21 Electric quadrupole. Figure 22-39 shows an electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Show that the value of E on the axis of the quadrupole for a point P a distance z from its center (assume z d) is given by
in which Q (= 2qd2) is known as the quadrupole moment of the charge distribution.
••10 In Figure 22-31, the four particles are fixed in place and have charges q1 = q2 = +5e, q3 = +3e, and q4 = –12e. Distance d = 5.0 mm. What is the magnitude of the net electric field at point P due to the particles?
••19 Figure 22-38 shows an electric dipole. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the dipole's electric field at point P, located at distance r d?
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