Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 3.3, Problem 3.13P
Find the potential in the infinite slot of Ex. 3.3 if the boundary at
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Students have asked these similar questions
Consider the geometry shown in the figure below. The lengths of the plates in the x and z
directions are ∞o. The width of plate 1 in the y direction is L=2. The potential on plates 2 and 3
are 0. The potential on plate 1 is V, = sin²
(1) Use separation of variables to find the potential V(x, y). Keep up to 3rd terms.
(2) Plot V(x = 0, y) as a function of y.
(3) Plot V(x, y = 1) as a function of x.
y
L=2
V.(y)
-Z
Plate 1
0
V=0
V=0
Plate 2
Plate 3
X
For problem 11 of the text,
calculate the potential in pixpoV at a point r = 0.398 R from the center of the sphere. (5 sig figs)
2. 2 A circular portion is cut from a nonconducting disk of radius R₂ = 15.0 cm, with radius R₁ = 4.0
cm measured from the origin of coordinates. The resulting disk, presented in the figure, is loaded
its surface with +3Q uniformly, with Q = 4.3 pc.
R₂
R₁
B
I
Then, find the value of the electric potential generated by the disk at point A, located at 20.0 cm
from the origin of the coordinate system.
And, if an object charged (considered as a point charge) with -1.8 µC is placed on the point A and
moves to point B, located 24.0 cm from the origin of the system of coordinates, what is the
minimum work required to move the charged object from A to B?
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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- An inverted hemispherical shell of radius R carries a uniform surface charge density ps. Find the potential difference between the point P2(0,0,R) and the center P1(0,0,0). Fig. 3arrow_forwardConsider the potential distribution V = 5r² sin 0 sin ø. Find: Py everywhere i. ii. The energy required to move 2 µc from A(x=3, y-4, z=5) to B(x=6, y=8, z=10)arrow_forwardA total charge of 36 uC is distributed uniformly throughout the surface of a 20 mm radius conducting sphere. What is the electric potential at a point 9 mm from the center of the sphere? Express your answer in MV.arrow_forward
- Problem 3.01. (a) Find the electric field between two plates which are separated along the y-axis Ay = 6.00 mm, where the bottom plate has a potential V₂ = 150. mV and the top plate has a potential V₁ = 5.00 mV. (b) What is the potential at a distance Ay' = 2.00 um from the bottom plate?arrow_forward6. 1. Consider circle with linear charge density λ = 1nC/cm and radius of 1 cm (like the one discussed in the class and shown in the figure below). This time assume that there are 2 of these charged circles of identical size and charge density, parallel with each other, both centered on the z-axis 2 cm apart. What is the potential on the Z-axis half way between the circles? Segment i with charge ΔΩ R O R² + z² What is the potential here? ........>> Your answer:arrow_forwardA sphere of radius a has potential (sin 2θ)( cos ϕ) on its surface. Find the potential at all points outside the sphere.arrow_forward
- Within the cylinder p = 2, 0 < z < 1, the potential is given by V = 50 + 100p + 150p sin V. a. Find V, E, D, and pv at P(,) in free space: b. How much charge lies within the cylinder.arrow_forward3. A cylindrical capacitor consists of a cylinder of radius R, surrounded by a coaxial cylinder shell of inner radius R.(see Fig.3 below, R. > R,). Both cylinders have length L which we assume is much greater than the separation of the cylinders R. – R,, so that we can neglect any end effects. Now the capacitor is charged (by connecting it to a battery) so that the inner cylinder carries a charge +Q and the other one a charge -Q. Note that charges are only distributed over the outer surface of the inner cylinder and the inner surface of the outer cylinder, because of electrostatic equilibrium for these metal conductors; as a result, the electrostatic field only exists in the empty space between two cylinders. Determine: (a). The electric field E(r) as a function of the radius r measured with respect to the central axis of the cylinders. [hint: draw a proper Gaussian surface and then use Gauss's law.] (b). The potential difference (voltage) V between two cylinders. (c). The capacitance…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
- Set up, but do not evaluate, an integral for the electric potential a distance R from the centre of a uniformly charged sphere of radius Ro. You may assume R> Ro.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) 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_forward-V: +V -V: The potential on the above sphere is +V for -45 <0 < 45° and -V everywhere else. Find the potential for small r (hint: Legendre polynomials may be useful) 2. Find the potential for large r 1. These may be useful: 3x2 – 1 Po(x) = 1; P(x) = x; P2(x) 21 +1arrow_forward
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