Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 21, Problem 15P
To determine
The motion of the dipole moment.
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ELECTRIC FIELD OF A DIPOLE
Given an electric dipole as shown in the Figure below, (1) show that for r>>a this dipole creates a field E with Ex and Eycomponents given below; and (2) show that this expression of E can also be written in polar coordinates.
Compute for the work done, in millijoules, in moving a 8-nC charge from A(0, 0, 1) m to B(0, 0, 7) m against the electric field due to a ring charge of radius 9 m on the plane z = 0 centered at the origin. The ring has a total charge of 8 mC.
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Chapter 21 Solutions
Physics for Scientists and Engineers
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- Compute for the work done, in millijoules, in moving a 8-nC charge from A(4, -4, 1) m to B(1, 4, 6) m against the electric field due to a ring charge of radius 9 m on the plane z = 0. The ring has a total charge of 6 mC.arrow_forwardCompute for the work done, in millijoules, in moving a 4-nC charge from A(4, -2, -4) m to B(3, -1, 2) m against the electric field due to a disk charge of radius 2 m on the plane x = 0. The disk has a total charge of 8 mC.arrow_forwardFind the ratio of q/Q for the E-field to be zero at adistance of z = 3.20R for the charge distributionand geometry of problem #30 of the text. a isthe charge on the LARGER ring. Q is the chargeon the SMALLER ring. Answer in 5 Significant Figures!!arrow_forward
- Find the ratio of q/Q for the E-field to be zero at adistance of z = 3.59R for the charge distributionand geometry of problem #30 of the text. a isthe charge on the LARGER ring. Q is the chargeon the SMALLER ring. Answer in 5 Significant Figures!!arrow_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_forwardCompletely solvearrow_forward
- Show that the energy of an ideal dipole p in an external electric field E is U = -p E Start by calculating the energy of a physical dipole of charges +ą separated by a displacement a, with p qa. Then take the limit a → 0, q + o with qa constant (equal to p).arrow_forwardCompute for the work done, in millijoules, in moving a 9-nC charge from A(-1, 1, 3) m to B(-1, -4, 9) m against the electric field due to a ring charge of radius 6 m on the plane z = 0. The ring has a total charge of 6 mC. use 4 decimal answerarrow_forwardShown below (Figure 1) is an electric dipole with equal charges +Q and –Q separated by a distance d. The dipole is free to rotate or move. Consider the following information: The dipole sits inside an electric field with |E| > 0. The dipole feels the largest torque possible. When rotated from its original orientation and released, the dipole moves back towards the original orientation. (a) On the picture below, sketch field lines corresponding to an external electric field that is compatible with this description. (b) Qualitatively, describe what would happen if the external field is shifted by 90 degreesarrow_forward
- In empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 4 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point A (5,0,0). ke = 1 / 4πεWrite numerically the components of the electrostatic field in terms of the given quantities.arrow_forwardCompute for the work done, in millijoules, in moving a 9-nC charge radially away from the center from a distance of 4 m to a distance of 9 m against the electric field inside a solid insulating sphere of radius 13 m and total charge 8 mC.arrow_forwardNewton's law of gravity and Coulomb's law are both inverse-square laws. Consequently, there should be a "Gauss's law for gravity." The electric field was defined as E = Fon q/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g→ of a point mass? Write your answer using the unit vector r^, but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive. Express your answer in terms of the variables M, r, unit vector r^, and the gravitational constant G. Use the 'unit vector' button to denote unit vectors in your answer. A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as ρ=ρ0(1−r/2R), where ρ0 is the density at the center. Determine ρ0 in terms of M and R. Gauss's law for gravity: integral ∮g →⋅ dA =−4πGMinFind an expression for the gravitational field strength inside the planet at distance r < R.arrow_forward
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