Concept explainers
You are working for the summer at a research laboratory. Your research director has devised a scheme for holding small charged particles at fixed positions. The scheme is shown in Figure P23.35. A large insulating sphere of radius a carries a total positive charge Q with a uniform volume charge density. A very thin tunnel is drilled through a diameter of the sphere and two small spheres with charge q are placed in the tunnel. These spheres are represented by the blue dots in the figure. They find equilibrium positions at a distance of r on either side of the center of the sphere. Your research director has had great success with this scheme. (a) Determine the specific value of r at which equilibrium exists. (b) Your research director asks you to see if he can extend the system as follows. Determine if it is possible to add transparent plastic tubes as extensions of the tunnel and have the small spheres be in equilibrium at a position for which r > a.
Figure P23.35
Trending nowThis is a popular solution!
Chapter 23 Solutions
Physics:f/sci.+engrs.,ap Ed.
- The infinite sheets in Figure P25.47 are both positively charged. The sheet on the left has a uniform surface charge density of 48.0 C/m2, and the one on the right has a uniform surface charge density of 24.0 C/m2. a. What are the magnitude and direction of the net electric field at points A, B, and C? b. What is the force exerted on an electron placed at points A, B, and C? FIGURE P25.47arrow_forwardA very long, thin wire fixed along the x axis has a linear charge density of 3.2 C/m. a. Determine the electric field at point P a distance of 0.50 m from the wire. b. If there is a test charge q0 = 12.0 C at point P, what is the magnitude of the net force on this charge? In which direction will the test charge accelerate?arrow_forwardIn Figure P24.49, a charged particle of mass m = 4.00 g and charge q = 0.250 C 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. FIGURE P24.49arrow_forward
- 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.arrow_forwardFigure P23.49 shows two identical small, charged spheres. One of mass 4.0 g is hanging by an insulating thread of length 20.0 cm. The other is held in place and has charge q1 = 3.6 C. The thread makes an angle of 18 with the vertical, resulting in the spheres being aligned horizontally, a distance r apart. Determine the charge q2 on the hanging sphere. Figure P23.49arrow_forwardA conducting sphere of radius r1 = 0.27 m has a total charge of Q = 2.6 μC. A second uncharged conducting sphere of radius r2 = 0.34 m connects to the first by a thin conducting wire. The spheres are separated by a very large distance compared to their size. a. What is the total charge on sphere two Q2 after they are connected, in coulombs? b. What is the surface charge density of the second sphere, σ2, after they are connected in coulombs per square meter?arrow_forward
- I FIGURE P27.40 shows a solid metal sphere at the center of a hol- low metal sphere. What is the total charge on (a) the exterior of the inner sphere, (b) the inside surface of the hollow sphere, and (c) the exterior surface of the hollow sphere? Conducting spheres 15,000 N/C 5 cm 10 cm 15,000 N/C cm 8 cm FIGURE P27.40 17 cmarrow_forwardA 3-D printer lays down a semicircular arc of positively charged plastic with a radius R = 2.8 cm, and a linear charge density of λ = +1.6 μC/m. After the printer has finished the arc, the stylus moves to the center of the arc as shown. The minute segment of the plastic arc highlighted in the diagram subtends an angle dθ. 1. Input an expression for the charge dq on the segment of size dθ in terms of given parameters. 2. Input an expression for the electric field vector, dE, generated at the center of the arc by the minute segment of plastic subtending the arc dθ. Express your answer in terms of given parameters, the Coulomb constant k, and the unit vectors i and j. 3. Evaluate the expression from part (b) as an indefinite integral to determine the x-component of the electrical field, Ex, at the center of the arc generated by the entire line of charged plastic. 4. Select the limits of integration that would result in the correct calculation of the electric field at the center of the…arrow_forwardYou are working in a manufacturing plant. In one particular machine, electric charges are suspended above a uniformly charged disk of radius R. The disks become corroded rapidly and must be replaced daily. Your supervisor comes to you one day and tells you that he wants to replace the disks with much cheaper washers of radius R with a concentric hole of radius R/4. He asks you to determine by what factor the charge on the disk must be increased so that a uniform charge on the washer would provide the same electric field at a distance x = R on the central axis as did the disk Answer should be in the form qwasher/qdiskarrow_forward
- a. Two small, positively charged spheres experience a mutual repulsive force of 1.52 N when their centers are 20 cm apart. The sum of the charges on the two spheres is 6 µC. What is the electric charge on each sphere?arrow_forwardTwo identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconducting walls, the beads move, and at equilibrium, they are a distance d apart (Fig. P22.44). (a) Determine the charge q on each bead. (b) Determine the charge required for d to become equal to 2Rarrow_forwardTwo small insulating spheres with radius 6.50×10−2 m are separated by a large center-to-center distance of 0.600 m . One sphere is negatively charged, with net charge -2.40 μC , and the other sphere is positively charged, with net charge 3.95 μC . The charge is uniformly distributed within the volume of each sphere. a. What is the magnitude E of the electric field midway between the spheres? Take the permittivity of free space to be ϵ0 = 8.85×10−12 C2/(N⋅m2) .arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning