Principles of Physics: A Calculus-Based Text

5th Edition

ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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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.

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A Van de Graaff generator is charged so that a proton at its surface accelerates radially outward at 1.52 1012 m/s3. Find (a) the magnitude of the electric force on the proton at that instant and (b) the magnitude and direction of the electric field at the surface of the generator.

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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

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A Figure P23.65 shows two identical conducting spheres, each with charge q, suspended from light strings of length L. If the equilibrium angle the strings make with the vertical is , what is the mass m of the spheres? Figure P23.65

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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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Two large, parallel metal plates, each of area A, are oriented horizontally and separated by a distance 3d. A grounded conducting wire joins them, and initially each plate carries no charge. Now a third identical plate carrying charge Q is inserted between the two plates, parallel to them and located a distance d from the upper plate as shown in Figure P20.84. (a) What induced charge appears on each of the two original plates? (b) What potential difference appears between the middle plate and each of the other plates? Figure P20.84

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A uniformly charged ring of radius R = 25.0 cm carrying a total charge of 15.0 C is placed at the origin and oriented in the yz plane (Fig. P24.54). A 2.00-g particle with charge q = 1.25 C, initially at the origin, is nudged a small distance x along the x axis and released from rest. The particle is confined to move only in the x direction. a. Show that the particle executes simple harmonic motion about the origin. b. What is the frequency of oscillation for the particle? Figure P24.54

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Identical thin rods of length 2a carry equal charges +Q uniformly distributed along their lengths. The rods lie along the x axis with their centers separated by a distance b 2a (Fig. P23.30). Show that the magnitude of the force exerted by the left rod on the right one is F=(keQ24a2)ln(b2b24a2) Figure P23.50

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The dome of a Van de Graaff generator receives a charge of 2.0 104 C. Find the strength of the electric field (a) inside the dome, (b) at the surface of the dome, assuming it has a radius of 1.0 m, and (c) 4.0 in front the center of the dome. Hint: See Section 15.5 to review properties of conductors in electrostatic equilibrium. Also, note that the points on the surface are outside a spherically symmetric charge distribution; the total charge may be considered to be located at the center of the sphere.

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A 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.

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An infinite line of positive charge lies along the y axis, with charge density = 2.00 C/m. A dipole is placed with its center along the x axis at x = 25.0 cm. The dipole consists of two charges 10.0 C separated by 2.00 cm. The axis of the dipole makes an angle of 35.0 with the x axis, and the positive charge is farther from the line of charge than the negative charge. Find the net force exerted on the dipole.

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