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) +

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 9P: Given two particles with 2.00-C charges as shown in Figure P20.9 and a particle with charge q = 1.28...

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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.
The three charged particles in Figure P25.22 are at the vertices of an isosceles triangle (where d = 2.00 cm). Taking q = 7.00 C, calculate the electric potential at point A, the midpoint of the base.
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 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.
A research Van de Graaff generator has a 2.00-rn- diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (C) An oxygen atom with three missing electrons is released near the Van de Graatf generator. What is its energy in MeV at this distance?
What is the potential 0.530 x 10-10 m from a proton (the average distance between the proton and electron in a hydrogen atom)?
An amoeba has 1.001016protons and a net charge of 0.300 pC. (a) How many fewer electrons are there than protons? (b) If you paired them up, what fraction of the protons would have no electrons?
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) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in Figure P16.13. (b) Repeat if the 2.00-C charge is replaced with a charge of 2.00 C. Figure P16.13 Problems 13 and 14.
(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) A uniformly charged cylindrical shell with no end caps has total charge Q, radius R, and length h. Determine the electric potential at a point a distance d from the right end of the cylinder as shown in Figure P24.51. Suggestion: Use the result of Example 24.5 by treating the cylinder as a collection of ring charges. (b) What If? Use the result of Example 24.6 to solve the same problem for a solid cylinder. Figure P24.51
The electric potential inside a charged spherical conductor of radius R is given by V = keQ/R, and the potential outside is given by V = keQ/R, Using Er = dV/dr, derive the electric field (a) inside and (b) outside this charge distribution.