1. Consider three protons (each with a charge of +lel) positioned on the three corners of a square with a side length of a. Then, from infinity to the origin, an electron (-lel) is brought. a Infinity to zero. How much work must be done by the electric field to bring the electron from infinity to the origin? OA. ke² ² O B. (2 + √²) (2+1/2²) kle|² a O C. kle² (2-√2) - a 2. Assume that the three protons and the electron are originally at infinity. Then they are put together so that the three protons are at (0,2), (a, a), and (a,0), where a > 0, and the electron is at the origin. What is the electric potential energy involved in putting them together? OA 4k|e² (4+ √2) a 08. 0 OC 4kcl a a O 0. Ale² a OA 2√2kjel a OB. √2kel a OC. -√2klel a 3. What is the potential at the center of the square formed by the four charged particles assembled in Item 2? OD. 2k|cl G -(4+ √2) +

1. Consider three protons (each with a charge of +lel) positioned on the three corners of a square with a side length of a. Then, from infinity to the origin, an electron (-lel) is brought. a Infinity to zero. How much work must be done by the electric field to bring the electron from infinity to the origin? OA. ke² ² O B. (2 + √²) (2+1/2²) kle|² a O C. kle² (2-√2) - a 2. Assume that the three protons and the electron are originally at infinity. Then they are put together so that the three protons are at (0,2), (a, a), and (a,0), where a > 0, and the electron is at the origin. What is the electric potential energy involved in putting them together? OA 4k|e² (4+ √2) a 08. 0 OC 4kcl a a O 0. Ale² a OA 2√2kjel a OB. √2kel a OC. -√2klel a 3. What is the potential at the center of the square formed by the four charged particles assembled in Item 2? OD. 2k|cl G -(4+ √2) +

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter7: Electric Potential

Section: Chapter Questions

Problem 96AP: Your friend gets really excited by the idea of making a lightning rod or maybe just a sparking toy...

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A 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.
Three charges are situated at corners of a rectangle as in Figure P16.13. How much work must an external agent do to move the 8.00-C charge to infinity? Figure P16.13 Problems 13 and 14.
A simple and common technique for accelerating electrons is shown in Figure 7.46, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving, (a) Calculate the acceleration of the electron if the field strength is 2.50104 N/C . (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole. Figure 7.46 Parallel conducting plates with opposite charges on them create a relatively uniform electric field used to accelerate electrons to the right. Those that go through the hole can be used to make a TV or computer screen glow or to produce X- rays.
A point charge of q=50108 C is placed at the center of an uncharged spherical conducting shell of inner radius 6.0 cm and outer radius 9.0 cm. Find the electric potential at (a) r = 4,0cm, (b) r = 8.0 cm, (c) r — 12.0 cm.
Your friend gets really excited by the idea of making a lightning rod or maybe just a sparking toy by connecting two spheres as shown in Figure 7.39, and making R2so small that the electric field is greater than the dielectric strength of air, just from the usual 150 V/m electric field near the surface of the Earth. If R1is 10 cm. how small does R2to be, and does this seem practical? (Hint: recall the calculation for electric field at the surface of a conductor from Gauss's Law.)
From Gauss's law, the electric field set up by a uniform line of charge is E=(20r)r where r is a unit vector pointing radially away from the line and is the linear charge density along the line. Derive an expression for the potential difference between r = r1, and r = r2.
A common demonstration involves charging a rubber balloon, which is an insulator, by rubbing it on your hair and then touching the balloon to a ceiling or wall, which is also an insulator. Because of the electrical attraction between the charged balloon and the neutral wall, the balloon slicks to the wall. Imagine now that we have two infinitely large, Hat sheets of insulating material. One is charged, and the other is neutral, lf these sheets are brought into contact, does an attractive force exist between them as there was for the balloon and the wall?
(a) How strong is the attractive force between a glass rod with a 0.700 C charge and a silk cloth with a 0.600 C charge, which are 12.0 cm apart, using the approximation that they act like point charges? (b) Discuss how the answer to this problem might be affected if the charges are distributed over some area and do not act like point charges.
(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in figure 18.46 is zero if the charges on the four comers are exactly equal. (b) Show that this is also true for any combination of charges in which qa= qd and qa = qc
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.
(i) A metallic sphere A of radius 1.00 cm is several centimeters away from a metallic spherical shell B of radius 2.00 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next, the two objects are joined by a long, thin, metallic wire (as shown in Fig. 25.19), and finally the wire is removed. How is the charge shared between A and B? (a) 0 on A. 450 nC on B (b) 90.0 nC on A and 360 nC on B, with equal surface charge densities (c) 150 nC on A and 300 nC on B (d) 225 nC on A and 225 nC on B (e) 450 nC on A and 0 on B (ii) A metallic sphere A of radius 1 cm with charge 450 nC hangs on an insulating thread inside an uncharged thin metallic spherical shell B of radius 2 cm. Next, A is made temporarily to touch the inner surface of B. How is the charge then shared between them? Choose from the same possibilities. Arnold Arons, the only physics teacher yet to have his picture on the cover ol Time magazine, suggested the idea for this question.
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.