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Review. In an electron microscope, there is an electron gun that contains two charged metallic plates 2.80 cm apart. An electric force accelerates each electron in the beam from rest to 9.60% of the
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- A proton is released from rest at the origin in a uniform electric field in the positive x direction with magnitude 850 N/C. What is the change in the electric potential energy of the protonfield system when the proton travels to x = 2.50 m? (a) 3.40 1016 J (b) 3.40 1016 J (c) 2.50 1016 J (d) 2.50 1016 J (e) 1.60 1019 Jarrow_forwardTwo particles, with charges of 20.0 nC and 20.0 nC, are placed at the points with coordinates (0, 4.00 cm) and (0, 4.00 cm) as shown in Figure P20.19. A particle with charge 10.0 nC is located at the origin. (a) Find the electric potential energy of the configuration of the three fixed charges. (b) A fourth particle, with a mass of 2.00 1013 kg and a charge of 40.0 nC, is released from rest at the point (3.00 cm, 0). Find its speed after it has moved freely to a very large distance away.arrow_forwardA proton is located at the origin, and a second proton is located on the x-axis at x = 6.00 fm (1 fm = 10-15 m). (a) Calculate the electric potential energy associated with this configuration. (b) An alpha particle (charge = 2e, mass = 6.64 1027 kg) is now placed at (x, y) = (3.00, 3.00) fm. Calculate the electric potential energy associated with this configuration. (c) Starting with the three-particle system, find the change in electric potential energy if the alpha particle is allowed to escape to infinity while the two protons remain fixed in place. (Throughout, neglect any radiation effects.) (d) Use conservation of energy to calculate the speed of the alpha particle at infinity. (e) If the two protons are released from rest and the alpha panicle remains fixed, calculate the speed of the protons at infinity.arrow_forward
- A constant electric field accelerates a proton from rest through a distance of 2.00 m to a speed of 1.50 105 m/s. (a) Find the change in the protons kinetic energy. (b) Find the change in the systems electric potential energy. (c) Calculate the magnitude of the electric field.arrow_forwardFour charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = 2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy as their separations become infinite? FIGURE P26.14 Problems 14, 15, and 16.arrow_forwardFour charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = +2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy?arrow_forward
- Two particles each with charge +2.00 C are located on the x axis. One is at x = 1.00 m, and the other is at x = 1.00 m. (a) Determine the electric potential on the y axis at y = 0.500 m. (b) Calculate the change in electric potential energy of the system as a third charged particle of 3.00 C is brought from infinitely far away to a position on the y axis at y = 0.500 m.arrow_forwardA small rigid object carries positive and negative 3 .50-nC charges. It is oriented so that the positive charge has coordinates (1.20 mm, 1.10 mm) and the negative charge is at the point (1.40 mm. 1.30 nun), (a) Find the electric dipole moment of the object. The object is placed in an electric field E = (7.80 103 i 4.90 103 j ) N/C. (b) Find the torque acting on the object, (c) Find the potential energy of the object-field system when the object is in this orientation, (d) Assuming the orientation of the object can change. find the difference between the maximum and minimum potential energies of the system.arrow_forwardFIGURE P26.14 Problems 14, 15, and 16. Four charged particles are at rest at the corners of a square (Fig. P26.14). The net charges are q1 = q2 = 2.65 C and q3 = q4 = 5.15 C. The distance between particle 1 and particle 3 is r13 = 1.75 cm. a. What is the electric potential energy of the four-particle system? b. If the particles are released from rest, what will happen to the system? In particular, what will happen to the systems kinetic energy as their separations become infinite?arrow_forward
- A spherical balloon contains a positively charged particle at its center. As the balloon is inflated to a larger volume while the charged particle remains at the center, which of the following are true? (a) The electric potential at the surface of the balloon increases. (b) The magnitude of the electric field at the surface of the balloon increases. (c) The electric flux through the balloon remains the same. (d) None of these.arrow_forwardGiven two particles with 2.00-C charges as shown in Figure P20.9 and a particle with charge q = 1.28 1018 C at the origin, (a) what is the net force exerted by the two 2.00-C charges on the test charge q? (b) What is the electric field at the origin due to the two 2.00-C particles? (c) What is the electric potential at the origin due to the two 2.00-C particles? Figure P20.9arrow_forwardThe labeled points in Figure 20.4 are on a series of equipotential surfaces associated with an electric field. Rank (from greatest to least) the work done by the electric field on a positively charged particle that moves from to , from to , from to , and from to . Figure 20.4 (Quick Quiz 20.2) Four equipotential surfaces.arrow_forward
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