Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 3.2, Problem 3.12P
To determine
The electric potential at every point of two long straight copper pipes.
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Problem 2.20 One of these is an impossible electrostatic field. Which one?
(a) E =k[xyÂ+2yzý+3xz2];
(b) E = k[y² + (2xy + z²)ý + 2yz 2).
Here k is a constant with the appropriate units. For the possible one, find the potential, using
the origin as your reference point. Check your answer by computing VV. [Hint: You must
select a specific path to integrate along. It doesn't matter what path you choose, since the
answer is path-independent, but you simply cannot integrate unless you have a particular path
in mind.]
Figure 2.87
For Prob. 2.23.
2.10 Determine i, and iz in the circuit of Fig. 2.74.
4 A
8.
Figure 2.74
For Prob. 2.10.
For problem 4 part b in square centimeters using inner and outer radii of the spherical capacitor of a = 5.49 cm and b = 1.05 a, respectively. (Answer In 5 sig. figs.)
Chapter 3 Solutions
Introduction to Electrodynamics
Ch. 3.1 - Find the average potential over a spherical...Ch. 3.1 - Prob. 3.2PCh. 3.1 - Prob. 3.3PCh. 3.1 - Prob. 3.4PCh. 3.1 - Prob. 3.5PCh. 3.1 - Prob. 3.6PCh. 3.2 - Find the force on the charge +q in Fig. 3.14....Ch. 3.2 - (a) Using the law of cosines, show that Eq. 3.17...Ch. 3.2 - In Ex. 3.2 we assumed that the conducting sphere...Ch. 3.2 - A uniform line charge is placed on an infinite...
Ch. 3.2 - Two semi-infinite grounded conducting planes meet...Ch. 3.2 - Prob. 3.12PCh. 3.3 - Find the potential in the infinite slot of Ex. 3.3...Ch. 3.3 - Prob. 3.14PCh. 3.3 - A rectangular pipe, running parallel to the z-axis...Ch. 3.3 - A cubical box (sides of length a) consists of five...Ch. 3.3 - Prob. 3.17PCh. 3.3 - Prob. 3.18PCh. 3.3 - Prob. 3.19PCh. 3.3 - Suppose the potential V0() at the surface of a...Ch. 3.3 - Prob. 3.21PCh. 3.3 - In Prob. 2.25, you found the potential on the axis...Ch. 3.3 - Prob. 3.23PCh. 3.3 - Prob. 3.24PCh. 3.3 - Find the potential outside an infinitely long...Ch. 3.3 - Prob. 3.26PCh. 3.4 - A sphere of radius R, centered at the origin,...Ch. 3.4 - Prob. 3.28PCh. 3.4 - Four particles (one of charge q, one of charge 3q,...Ch. 3.4 - In Ex. 3.9, we derived the exact potential for a...Ch. 3.4 - Prob. 3.31PCh. 3.4 - Two point charges, 3qand q , arc separated by a...Ch. 3.4 - Prob. 3.33PCh. 3.4 - Three point charges are located as shown in Fig....Ch. 3.4 - A solid sphere, radius R, is centered at the...Ch. 3.4 - Prob. 3.36PCh. 3.4 - Prob. 3.37PCh. 3.4 - Here’s an alternative derivation of Eq. 3.10 (the...Ch. 3.4 - Prob. 3.39PCh. 3.4 - Two long straight wires, carrying opposite uniform...Ch. 3.4 - Prob. 3.41PCh. 3.4 - You can use the superposition principle to combine...Ch. 3.4 - A conducting sphere of radius a, at potential V0 ,...Ch. 3.4 - Prob. 3.44PCh. 3.4 - Prob. 3.45PCh. 3.4 - A thin insulating rod, running from z=a to z=+a ,...Ch. 3.4 - Prob. 3.47PCh. 3.4 - Prob. 3.48PCh. 3.4 - Prob. 3.49PCh. 3.4 - Prob. 3.50PCh. 3.4 - Prob. 3.51PCh. 3.4 - Prob. 3.52PCh. 3.4 - Prob. 3.53PCh. 3.4 - Prob. 3.54PCh. 3.4 - Prob. 3.55PCh. 3.4 - Prob. 3.56PCh. 3.4 - Prob. 3.57PCh. 3.4 - Find the charge density () on the surface of a...
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- In Fig. 1, two parallel-plate capacitors (with air between theplates) are connected to a battery. Capacitor 1 has a plate areaof 1.5 cm2and an electric field (between its plates) ofmagnitude 2000 V/m. Capacitor 2 has a plate area of 0.70 cm2and an electric field of magnitude 1500 V/m. What is the totalcharge on the two capacitors?arrow_forwardProblem 2.28 Use Eq. 2.29 to calculate the potential inside a uniformly charged solid sphere of radius R and total charge q. Compare your answer to Prob. 2.21.arrow_forwardA particle moves in a potential given by U(x) = -7 x3 + 2.1 x (J). Calculate the location of the stable equilibrium of this potential, in m. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forward
- 4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) P-I nC/m 20° z-0 plane (0, 3, 0) p-3 Pu=1.5 nC/m 10° p-1.6 10° p-3.5 PacI nCim? 20 FIGURE 4.1Iarrow_forwardW = 'fD-Edr. (4.58)arrow_forwardConsider a rod of length L carrying a charge of q distributed uniformly over its length. Where applicable, let V(r → ∞) = 0. Hint q a. What is the voltage V at point P (at distance a away from the near end of the rod) due to the charge over the length of the rod? Express your answer in terms of given parameters (L,q,a) and physical constants (ke, Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for (a) E = Vp = b. Calculate the electric field at point P by differentiating V with respect to a. Let positive sign of E indicate direction of electric field pointing away from the rod. Hint for (b) a Question Help: Message instructor Submit Question с MacBook Pro G Search or type URL ☆ +arrow_forward
- 4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. %3D (0, 5, 0)| PLA=A nC/m 20° z=0 plane (0, 3, 0) p= 3 PLB= 1.5 nC/m 10° 10° p=1.6 p= 3.5 Psc 1 nC/m2 20° FIGURE 4.11 See Prob. 20.arrow_forwardProblem 2.60 A point charge q is at the center of an uncharged spherical conducting shell, of inner radius a and outer radius b. Question: How much work would it take to move the charge out to infinity (through a tiny hole drilled in the shell)? [Answer: (q²/80) (1/a-1/b).]arrow_forward4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) PLA=A nC/m 20° z=0 plane (0, 3, 0) p=3 PLB=1.5 nC/m 10° 10° p= 1.6 p=3.5 Psc=1 nC/m² 20° FIGURE 4.11 See Prob. 20.arrow_forward
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