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(III) Two positive charges +Q are affixed rigidly to the x axis, one at x = +d and the other at x = −d. A third charge +q of mass m, which is constrained to move only along the x axis, is displaced from the origin by a small distance s << d and then released from rest. (a) Show that (to a good approximation) +q will execute
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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 P24.54arrow_forwardTwo identical point charges, each with charge +q, are fixed in space and separated by a distance "d". A third point charge -Q of mass "m" It can move freely and is initially at rest on the x-axis at a distance "x" +q d/2 0 d/2 +q -Q X Prove that for very small "x" (x<arrow_forward(c) Now consider a K+ ion (modelled as a single particle of mass 6.5 x 10-26 kg and charge +e) and a Cl- ion (modelled as a single particle of mass 5.9 x 10-26 kg and charge -e), with the two particles being separated by 1.0 x 10-9 m and in the absence of other forces. Compare the strength and direction of the gravitational and electrostatic forces between the two particles. (d) Figure 3 (on page 9) shows field lines in the region containing two particles, both of which are charged and have mass. On the basis of information in Figure 3 alone: XXarrow_forwardAn electron and proton are separately placed at rest midway between two oppositely charged metal plates. (a) Which way will the electron accelerate? (b) Which way will the proton accelerate? (c) Which particle, if either, will acquires more kinetic energy just before striking a plate? (d) What is the ration of their velocities just before they strike the plates?arrow_forwardTwo identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge −Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between those charges. (a) Show that if x is small compared with d, the motion of −Q is simple harmonic along the perpendicular bisector. (b) Determine the period of that motion. (c) How fast will the charge −Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a<<d from the midpoint?arrow_forwardP.3-15 Three charges (+q, -2q, and +q) are arranged along the z-axis at z = d/2, z = 0, and z = -d/2, respectively. Problems a) Determine V and E at a distant point P(R, 0, ).arrow_forwardA light, unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and then released at the same moment. The system then oscillates on a frictionless, horizontal table. The spring has a bit of internal kinetic friction, so the oscillation is damped. The particles eventually stop vibrating when the distance between them is 3d. Assume the system of the spring and two charged particles is isolated. Find the increase in internal energy that appears in the spring during the oscillations.arrow_forwardTwo equal point charges q are fixed in (d, 0, 0) and (−d, 0, 0); a third point charge−Q of mass m is free to move along the y-axis. Calculate the frequency of small oscillationsaround the origin. Hint: The differential equation of a harmonic oscillator, x(t), isdx^2/dt^2 + ω^2x = 0arrow_forwardA “pure” dipole p is situated at the origin, pointing in the z-direction. (i) What is the force on a point charge q at (a, 0, 0) (Cartesian coordinates)?(ii) What is the force on q at (0, 0, a)?(iii) How much work does it take to move q from (a, 0, 0) to (0, 0, a)?arrow_forwardFour equal charges, q, are fixed at the corners of a square of side a in the xy-plane centered on the origin. A bead of mass m and charge -q is positioned at the origin. A thin, frictionless string along the z-axis threads the bead, thus restricting its mo- tion to the z-axis. The bead is then displaced from the origin by a small amount Zo < 0 and released from rest. Show that the bead undergoes simple harmonic motion (to a very good approximation), and derive an expression for its period of oscillation in terms of known parameters.arrow_forwardFind the dipole moment of the given four charge arrangement shown below. (a,a) (0, a) -2q q (0,0) (a) p=0 (b) p = qay (c) p = 2qa x (d) p = qax 2q -9 (a,0)arrow_forward(c) An electric dipole consists of 0.003 kg spheres charged to ∓3e-09 C at the ends of a 0.16 m long non-conducting rod of mass 0.006 kg (don't try to look up "electric dipole", it wont help you. For the sake of this problem, it is just a fancy word for what I just described). The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular to a uniform electric field with a field strength 1000 V/m, then released. i.What is the dipole's angular velocity (in rad/s) at the instant it is aligned with the electric field? (HINT: Look up the moment of inertia of the rotating rod about its center and don't forget the rotational kinetic energy term (along with the other terms) when you set up your conservation of energy problem). a)0.0534 b)0.446 c)0.289 d)0.119 e)0.137 f)0.205 (d) Four 1.9e-08 C charges are held in location to form a perfect square with sides of length 0.1 m. Two of the charges from opposing corners are released simultaneously, the other two are…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
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