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- Assume the charged objects in Figure OQ19.15 are fixed. Notice that there is no sight line from the location of q2 to the location of q1. If you were at q1, you would be unable to see q2 because it is behind q3. How would you calculate the electric force exerted on the object with charge q1? (a) Find only the force exerted by q2 on charge q1. (b) Find only the force exerted by q3 on charge q1. (c) Add the force that q2 would exert by itself on charge q1 to the force that q3 would exert by itself on charge q1. (d) Add the force that q3 would exert by itself to a certain fraction of the force that q2 would exert by itself. (e) There is no definite way to find the force on charge q1. Figure OQ19.15arrow_forwardTwo 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?arrow_forwardA sphere has a net charge of 8.05 nC, and a negatively charged rod has a charge of 6.03 nC. The sphere and rod undergo a process such that 5.00 109 electrons are transferred from the rod to the sphere. What are the charges of the sphere and the rod after this process?arrow_forward
- A proton and an alpha particle (charge = 2e, mass = 6.64 1027 kg) are initially at rest, separated by 4.00 1015 m. (a) If they are both released simultaneously, explain why you cant find their velocities at infinity using only conservation of energy. (b) What other conservation law can be applied in this case? (c) Find the speeds of the proton and alpha particle, respectively, at infinity.arrow_forwardAn electroscope is a device used to measure the (relative) charge on an object (Fig. P23.20). The electroscope consists of two metal rods held in an insulated stand. The bent rod is fixed, and the straight rod is attached to the bent rod by a pivot. The straight rod is free to rotate. When a positively charged object is brought close to the electroscope, the straight movable rod rotates. Explain your answers to these questions: a. Why does the rod rotate in Figure P23.20? b. If the positively charged object is removed, what happens to the electroscope? c. If a negatively charged object replaces the positively charged object in Figure P23.20, what happens to the electroscope? d. If a charged object touches the top of the fixed conducting rod and is then removed, what happens to the electroscope?arrow_forwardA 1.75-nC charged particle located at the origin is separated by a distance of 0.0825 m from a 2.88-nC charged particle located farther along the positive x axis. Both particles are held at their locations by an external agent. a. What is the electrostatic force on the 2.88-nC particle? b. What is the electrostatic force on the 1.75-nC particle?arrow_forward
- You are working as an expert witness for an inventor. The inventor devised a system that allows an 85.0-kg human to hover above the ground at the surface of the Earth due to the repulsive force between a charge q applied to his body and the normal electric charge on the Earth. The normal charge on the Earth is such that the electric field is uniform from near the Earths surface, directed downward toward the surface, and is of magnitude 130 N/C at the location of the engineers experiments. Everything went well until the engineer tried a new experiment. He attempted to transfer the same amount of charge q to each of two experimental subjects standing next to each other, so they could hover and work close together on a task. The charged, hovering experimental subjects repelled each other and were injured as they flew away in opposite directions. Both experimental subjects are now suing the inventor for their injuries. The inventor is claiming that it is not his fault if the subjects find each other repulsive. To find out whether the inventor has a good defense, determine the initial acceleration of each subject if they are working 1.00 m apart.arrow_forwardAssume the charged objects in Figure OQ23.10 are fixed. Notice that there is no sight line from the location of q2 to the location of q1. If you were at q1, you would be unable to see q2 because it is behind q3. How would you calculate the electric force exerted on the object with charge q1? (a) Find only the force exerted by q2 on charge q1. (b) Find only the force exerted by q3 an charge q1. (c) Add the force that q2 would exert by itself on charge q1 to the force that q3 would exert by itself on charge q1. (d) Add the force that q3 would exert by itself to a certain fraction of the force that q2 would exert by itself. (e) There is no definite way to find the force on charge q1.arrow_forwardThree 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 OQ19.14arrow_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_forwardTwo point charges attract each other with an electric force of magnitude F. If the charge on one of the particles is reduced to one-third its original value and the distance between the particles is doubled, what is the resulting magnitude of the electric force between them? (a) 112F (b) 13F (c) 16F (d) 34F (e) 32Farrow_forwardAn electron with a speed of 3.00 106 m/s moves into a uniform electric field of magnitude 1.00 103 N/C. The field lines are parallel to the electrons velocity and pointing in the same direction as the velocity. How far does the electron travel before it is brought to rest? (a) 2.56 cm (b) 5.12 cm (c) 11.2 cm (d) 3.34 m (e) 4.24 marrow_forward
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