Charge Q = 4.00 μC is distributed uniformly over the volume of an insulating sphere that has radius R = 11.0 cm. A small sphere with charge q =+ 3.00 μC and mass 6.00×10^−5kg is projected toward the center of the large sphere from an initial large distance. The large sphere is held at a fixed position and the small sphere can be treated as a point charge. What minimum speed must the small sphere have in order to come within 8.00 cm of the surface of the large sphere?

Four balls, each with mass m, are connected by four nonconducting strings to form a square with side a as shown in Figure P25.74. The assembly is placed on a nonconducting. frictionless. horizontal surface. Balls 1 and 2 each have charge q, and balls 3 and 4 are uncharged. After the string connecting halls 1 and 2 is cut, what is the maximum speed of balls 3 and 4?

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.

A Two positively charged spheres with charges 4e and e are separated by a distance L and held motionless. A third charged sphere with charge Q is set between the two spheres and along the line joining them. The third sphere is in static equilibrium. What is the distance between the third charged sphere and the sphere that has charge 4e?

A particle with charge +q is at the origin. A particle with charge 2q is at x = 2.00 m on the x axis. (a) For what finite value(s) of x is the electric field zero? (b) For what finite value(s) of x is the electric potential zero?

Three charged particles are arranged on corners of a square as shown in Figure OQ19.14, with charge Q on both the particle at the upper left corner and the particle at the lower right corner and with charge +2Q on the particle at the lower left corner. (i) What is the direction of the electric field at the upper right corner, which is a point in empty space? (a) It is upward and to the right. (b) It is straight to the right. (c) It is straight downward. (d) It is downward and to the left. (e) It is perpendicular to the plane of the picture and outward. (ii) Suppose the +2 Q charge at the lower left corner is removed. Then does the magnitude of the field at the upper right corner (a) become larger, (b) become smaller, (c) stay the same, or (d) change unpredictably? Figure OQ19.14

A particle with charge 1.60 1019 C enters midway between two charged plates, one positive and the other negative. The initial velocity of the particle is parallel to the plates and along the midline between them (Fig. P26.48). A potential difference of 300.0 V is maintained between the two charged plates. If the lengths of the plates are 10.0 cm and they are separated by 2.00 cm, find the greatest initial velocity for which the particle will not be able to exit the region between the plates. The mass of the particle is 12.0 1024 kg. FIGURE P26.48

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?

Two 5.00-nC charged particles are in a uniform electric field with a magnitude of 625 N/C. Each of the particles is moved from point A to point B along two different paths, labeled in Figure P26.65. a. Given the dimensions in the figure, what is the change in the electric potential experienced by the particle that is moved along path 1 (black)? b. What is the change in the electric potential experienced by the particle that is moved along path 2 (red)? c. Is there a path between the points A and B for which the change in the electric potential is different from your answers to parts (a) and (b)? Explain. FIGURE P26.65 Problems 65, 66, and 67.

Consider the final arrangement of charged particles shown in Figure P26.7. What is the work necessary to build such an arrangement of particles, assuming they were originally very far from one another? FIGURE P26.7 Problems 7 and 28.