(II) Two point charges, Q1 = -32 µC and Q2 = +45 µC, are separated by a distance of 12 cm. The electric field at the point P (see Fig. 16–57) is zero. How far from Qj is P? Q1 Q2 12 cm P -32 μC +45 µC FIGURE 16-57 Problem 32.

(II) Determine the electric field É at the origin 0 in Fig. 16–58 due to the two charges at A and B. y |+26 µC A 8.0 cm -26 µC B 8.0 cm FIGURE 16-58 8.0 cm Problem 33.

(II) A charge of 6.00 mC is placed at each corner of a square 0.100 m on a side. Determine the magnitude and direction of the force on each charge.

(III) The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 16–39. Assume that the net average charge (due to electron sharing) indicated on H and N atoms has magnitude 0.2e and on the indicated C and O atoms is 0.4e. Assume also that atoms on each molecule are separated by 1.0 × 10-10 m. Estimate the net force between (a) a thymine and an adenine; and (b) a cytosine and a guanine. For each bond (red dots) consider only the three atoms in a line (two atoms on one mol- ecule, one atom on the other). (c) Estimate the total force for a DNA molecule containing 10° pairs of such molecules. Assume half are A-T pairs and half are C-G pairs.

(II) Two charged dust particles exert a force of 4.2 x 10-2 Non each other. What will be the force if they are moved sothey are only one-eighth as far apart?

(II) At each corner of a square of side l there are point charges of magnitude Q, 2Q, 3Q, and 4Q (Fig. 16–54). Determine the mag- 20 nitude and direction of the force on the charge 2Q. FIGURE 16–54 Problem 15. 4Q

•27 Go In Fig. 22-51, two curved plastic rods, one of charge +q and the other of +4 charge -q, form a circle of radius R = 8.50 cm in an xy plane. The x axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. If q = 15.0 pC, what are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the electric field E produced at P, the -9 Figure 22-51 Problem 27. center of the circle?

(2.)(II) Two equal point charges Q are located on the y axis at y = a and y = -a. (a) What is the force on a charge q located at (x, 0)? (b) For what value of x is the force a maximum? Make a rough plot of F(x), the force as a func- tion of x. (c) When x > a, what is the form of F(x)? (Hint: Use the binomial expansion (1+z)" = 1 + nz for small z.)

(I) A downward electric force of 6.4 N is exerted on a - 7.3µ C charge. Find the magnitude and direction of the electric field at the position of this charge.