In the figure below, a charged particle of mass m = 20 g and charge q = 0.250 mC is suspended in static equilibrium at the end of an insulating thread that hangs from a very long, charged, thin rod. The thread is 12.0 cm long and makes an angle of 35.0° with the vertical. Determine the linear charge density of the rod.

Two small spherical conductors are suspended from light-weight vertical insulating threads. The conductors are brought into contact (Fig. P23.50, left) and released. Afterward, the conductors and threads stand apart as shown at right. a. What can you say about the charge of each sphere? b. Use the data given in Figure P23.50 to find the tension in each thread. c. Find the magnitude of the charge on each sphere. Figure P23.50

Three charged spheres are at rest in a plane as shown in Figure P23.70. Spheres A and B are fixed, but sphere C is attached to the ceiling by a lightweight thread. The tension in the string is 0.240 N. Spheres A and B have charges qA = 28.0 nC and qB = 28.0 nC. What charge is carried by sphere C?

A Two positively charged particles, each with charge Q, are held at positions (a, 0) and (a, 0) as shown in Figure P23.73. A third positively charged particle with charge q is placed at (0, h). a. Find an expression for the net electric force on the third particle with charge q. b. Show that the two charges Q behave like a single charge 2Q located at the origin when the distance h is much greater than a. Figure P23.73 Problems 73 and 74.

Charges A, B, and C are arranged in the xy plane with qA = 5.60 C, qB = 4.00 C, and qC = 2.30 /C (Fig. P23.43). What are the magnitude and direction of the electrostatic force on charge B? Figure P23.43

Two small beads having positive charges q1 = 3q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q1 is at the origin. As shown in Figure P19.7, a third small, charged bead is free to slide on the rod. (a) At what position x is the third bead in equilibrium? (b) Can the equilibrium be stable?

A point charge +2Q is at the origin and a point charge Q is located along the x axis at x = d as in Figure P22.11. Find a symbolic expression for the net force on a third point charge +Q located along the y axis at y = d. Figure P22.11

A Figure P23.65 shows two identical conducting spheres, each with charge q, suspended from light strings of length L. If the equilibrium angle the strings make with the vertical is , what is the mass m of the spheres? Figure P23.65

Three small metallic spheres with identical mass m and identical charge +q are suspended by light strings from the same point (Fig. P23.55). The left-hand and right-hand strings have length L and make an angle with the vertical. What is the value of q in terms of k, g, m, L, and ? Figure P23.55

a. Figure 24.22A shows a rod of length L and radius R with excess positive charge Q. The excess charge is uniformly distributed over the entire outside surface of the rod. Write an expression for the surface charge density . Write an expression in terms of for the amount of charge dq contained in a small segment of the rod of length dx. b. Figure 24.22B shows a very narrow rod of length L with excess positive charge Q. The rod is so narrow compared to its length that its radius is negligible and the rod is essentially one-dimensional. The excess charge is uniformly distributed over the length of the rod. Write an expression for the linear charge density . Write an expression in terms of for the amount of charge dq contained in a small segment of the rod of length dx. Compare your answers with those for part (a). Explain the similarities and differences.