Concept explainers
SSM Electric quadrupole. Figure 22-46 shows a generic electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Show that the value of E on the axis of the quadrupole for a point P a distance z from its center (assume z ≫ d) is given by
in which Q (= 2qd2) is known as the quadrupole moment of the charge distribution.
Figure 22-46 Problem 21.
Trending nowThis is a popular solution!
Chapter 22 Solutions
Fundamentals of Physics Extended
Additional Science Textbook Solutions
Genetic Analysis: An Integrated Approach (3rd Edition)
Concepts of Genetics (12th Edition)
Microbiology: An Introduction
Chemistry: An Introduction to General, Organic, and Biological Chemistry (13th Edition)
Applications and Investigations in Earth Science (9th Edition)
Campbell Biology (11th Edition)
- A charged nonconducting rod, with a length of 3.52 m and a cross-sectional area of 5.94 cm2, lies along the positive side of an x axis with one end at the origin. The volume charge density p is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if p is (a) uniform, with a value of -2.46 µC/m³, and (b) nonuniform, with a value given by p = bx2, where b = -2.26 µC/m3? (a) Number Units (b) Number Unitsarrow_forwardConsider an electric dipole of moment p. Electric field at any point (r, 0) due to the dipole is given as (2 cos 0 î + sin 0 0), Value of: is 80 (a) kp 3kp -sin e î + cos 0 0 -2 cos 0 î + cos 0 0 (c) P -3 sin e î + 2 cos kp (d) -3 sin 0r+2 cos 0 0arrow_forward(a) Figure (a) shows a nonconducting rod of length L = 5.80 cm and uniform linear charge density λ = +4.87 pC/m. Take V = 0 at infinity. What is Vat point P at distance d= 7.50 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 4.87 pC/m. With V=0 at infinity, what is Vat P? L/2 (a) -L/2 L/21/2- (b)arrow_forward
- (a) Figure (a) shows a nonconducting rod of length L-5.20 cm and uniform linear charge density A= +5.99 pC/m. Take V = 0 at infinity. What is Vat point P at distance d = 8.20 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 5.99 pC/m. With V 0 at infinity, what is Vat P? L/2 L/2 –L/2 L/2- (a) (b) (a) Number Units V (b) Number Units Varrow_forwardConsider an electric dipole in free space located at the coordinates origin where dipole moment is pointing in the positive z-axis direction. If the voltage due to this dipole is 0.6 V at the point (r, 0, 4)=(0.2m, 2.4rad, 0.9rad), Dipole moment p in pC.m is: One possible correct answer is: -3.6163403761983 Corresponding electric field components in V/m are: 10 EX One possible correct answer is: 6 10 One possible correct answer is: -2.7480428690202 10 One possible correct answer is: 0arrow_forwardAn electric dipole located at the origin in free space has a moment p = 3āx - 2āy + āz nC.m, find (a) V at PA (2, 3, 4), (b) V at r=2.5, 0=30°, Ø = 40°. %3Darrow_forward
- (a) Figure (a) shows a nonconducting rod of length L = 5.40 cm and uniform linear charge density λ = +4.41 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 9.30 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 4.41 pC/m. With V= 0 at infinity, what is V at P? (a) Number i (b) Number i P ‡ ‡ ‡ ‡ + + + +‡‡ ‡ ‡‡ L/2 L/2 Units Units [+ + + ++++G ·L/2 L/2-arrow_forward(a) Figure (a) shows a nonconducting rod of length L = 9.00 cm and uniform linear charge density λ = +7.57 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 5.20 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 7.57 pC/m. With V = 0 at infinity, what is V at P? (a) Number i (b) Number i ·+· -L/2 (a) Units Units L/2 +‡ ‡ ‡+3= L/2 .Р (b) L/2arrow_forward(a) Figure (a) shows a nonconducting rod of length L = 8.00 cm and uniform linear charge density λ = +1.21 pc/m. Take V = 0 at infinity. What is V at point P at distance d = 7.40 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 1.21 pc/m. With V = 0 at infinity, what is V at P? 1/2 L/2- L/2 1/2 - (a) (b)arrow_forward
- d- d- + + P +9 -9-9 +9 -p +p Electric quadrupole. The figure shows an electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. What is the value of E on the axis of the quadrupole for a point P a distance z from its center (assume z >> d)? Take Q = 2qd² (which is known as the quadrupole moment of the charge distribution.) NOTE: Express your answer in terms of Q and z, using ε0 when needed. E =arrow_forwardThe magnitude of the electric fie ld at a distance r from a point charge O is equal to O/4πεor2. How close to a water molecule (of polarizability volume 1.48 x 1-30 m3) must a proton approach before the dipole moment it induces is equal to the permanent dipole moment of the molecule (1.85 D)?arrow_forwardL:05) Draw graph tooarrow_forward
- 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