W.: Consider a dipole in an external electric field Ë = Eoû where Eo is a constant. magnitudle of the dipole moment): For the four cases of orientation of the dipole (p is the (i) F pê (ii) = py (iii) =-pâ (iv) p= -py a. Find the potential energy of the dipole in this external field. Order your answers from highest to lowest potential energy. b. If the dipole were free to rotate in this external electric field, which orientation would be the equilibrium alignment? (as a hint, consider the analogy of a particle in the gravitational field of the earth; its potential energy increases with increasing altitude above the surface. If left free, in what direction of change of potential energy does it go?) at the origin of the coordinates meters from the

W.: Consider a dipole in an external electric field Ë = Eoû where Eo is a constant. magnitudle of the dipole moment): For the four cases of orientation of the dipole (p is the (i) F pê (ii) = py (iii) =-pâ (iv) p= -py a. Find the potential energy of the dipole in this external field. Order your answers from highest to lowest potential energy. b. If the dipole were free to rotate in this external electric field, which orientation would be the equilibrium alignment? (as a hint, consider the analogy of a particle in the gravitational field of the earth; its potential energy increases with increasing altitude above the surface. If left free, in what direction of change of potential energy does it go?) at the origin of the coordinates meters from the

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 82P

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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.
(a) What is the dipole moment of the configuration shown above? If Q=4.0C , (b) what is the torque on this dipole with an electric field of 4.0105N/Ci ? (c) What is the torque on this dipole with an electric field of 4.0105N/Ci ? (d) is the torque on this dipole with an field of 4.0105N/Cj ?
A water molecule is made up of two hydrogen atoms and one oxygen atom, with a total of 10 electrons and 10 protons. The molecule is modeled as a dipole with an effective separation d = 3.9 1012 m between its positive and negative particles. What is the electric potential energy stored in the dipole? What does the sign of your answer mean?
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.
Find an expression for the electric field at point A for the dipole source shown in Figure P24.17. Show that when y : d, the electric field is given by Ekp/y3.
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An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq. (a) At a point P, which is far from the dipole (r a), show that the electric potential is V=kepcosr2 (b) Calculate the radial component Er and the perpendicular component E of the associated electric field. Note that E = (1/r)(V/). Do these results seem reasonable for (c) = 90 and 0? (d) For r = 0? (e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r = (x2 + y2)1/2 and cos=y(x2+y2)1/2 (f) Using these results and again taking r a, calculate the field components Ex and Ey. Figure P24.48
From a distance of 10 cm, a proton is projected with a speed of v=4.0106 m/s directly at a large, positively charged plate whose charge density is =2.0105 C/m2. (See below.) (a) Does the proton reach the plate? (b) If not, how far from the plate does it turn around?
A water molecule is made up of two hydrogen atoms and one oxygen atom, with a total of 10 electrons and 10 protons. The molecule is modeled as a dipole with an effective separation d = 3.9 1012 m between its positive and negative charges. What is the magnitude of the water molecules dipole moment?
Review. Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.100 kg and 0.700 kg, and uniformly distributed charges 2.00 C and 3.00 C. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide? (b) What If? It the spheres were conductors, would the speeds be greater or less than those calculated in part (a)? Explain.
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