Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Textbook Question
Chapter 3.1, Problem 3.1P
Find the average potential over a spherical surface of radius R due toa point charge q located inside (same as above, in other words, only with
where Vcenteris the potential at the center due to all the external charges, and Qencisthe total enclosed charge.
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Lets say there is a spherical thin shell of radius a. It carries uniform surface chargewith a density of ps C/m2, (p is ro).
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Thank you for helping me with this practice.
A sphere of radius R, centered at the origin, carries charge densityρ(r, θ) = kRr^2(R − 2r ) cos θwhere k is a constant, and r, θ are the usual spherical coordinates. Find the approximate potential for points on the z axis, far from the sphere.
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d
a charge o, riting at origion- Sumounding
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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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- Consider a situation where a point charge q is located at the height of h above con- ducting ground. (The ground is in the potential V = 0.) (a) Calculate the force acting on the charge, assuming that the charge has a magnitude of q = +1 mC (which is 0.001 As), and the height is h = 1 m. What is the direction of the force? (Hint: the image principle might be helpful...) (b) Let's add another grounded conducting plane above the charge according to the figure, parallel to the original one, and the height d away from it. (In other words, now both planes are in the ground potential V = 0.) 2 Using again the image principle, find an equivalent charge constellation to replace the two conducting planes, such that the correct conductor boundary conditions are satisfied. (c) Compute the force acting on the charge in the case for d = 4h. Which direction is it? Is it larger or smaller than in the case of a single conductor?arrow_forwardA thin conducting disk of radius R, in a vacuum space, is placed on the a – y plane, and is held at a potential Vo. Find the electrostatic potential V (7) (that is the solution of the Laplace equation V'V = 0 under suitable BC) everywhere in space. Find also the areal charge density o on the disk.arrow_forward1.20P) An infinite line charge with line charge density of 2 located near an infinite, grounded conducting plane as shown in figure. Find the potential everywhere. Draw electric field lines and show equipotential surfaces. Calculate E field at the conductor surface due to the surface charges of o. Clearly indicate that, is the electric field and potential at the boundary surfaces are continuous or not (Explain your reasoning). The question has a linear charge density at the position x = a, y = b. ラメarrow_forward
- Show Your Solutions In free space, there are 2 concentric spherical surfaces with radii a and b. There is a constant volume charge density between 2 surfaces such that: (0; p=Po; aspsb (0; p>b pca a) BY USING POISSON'S EQUATION find the electric potential everywhere. b) BY USING POISSON'S EQUATION find the electric field vector everywherearrow_forwardGiven an electric potential of 1 _ q V= 4πεο Γ r find its corresponding electric field vector. Sol. Using the concept of potential gradient, we have È = - V Since we only have, radial direction (r). Then, the del-operator will be By substitution, we get Evaluating the differential, we, get the following 1 E-ATEO *(q/arrow_forwardConsider a potential field in cylindrical coordinates and a point P in the same coordinate system. coordinates given by: and the point P in the coordinates: Calculate: 100 V=- pcos($) [V] z²+1 p= 3m, = 60°, z = 2m. a) The potential V at point P. b) The field E at point P. c) The volumetric charge density p, in free space.arrow_forward
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- An annulus with an inner radius of a and an outer radius of b has charge density and lies in the xy-plane with its center at the origin, as shown in (Figure 1). Figure σ b K 1 a Z 0 X 1 of 1 y Part A Using the convention that the potential vanishes at infinity, determine the potential at all points on the z-axis. Express your answer in terms of the electric constant €0, o, a, b, and z. IVE ΑΣΦΑΝΟ V = Submit Part B Request Answer Determine the x-, y-, z-components of the electric field at all points on the z-axis by differentiating the potential. Enter your answers separated by commas. Express your answers in terms of the electric constant €0, o, a, b, x, y, and z. Ex, Ey, Ez = Submit V ΑΣΦ Request Answer ? Ć www ?arrow_forwardAn infinitely large horizontal plane carries a uniform surface charge density n = -0.280 nC/m². What is the electric field ✓? A proton is traveling in this field with initial speed strength in the region above the plane [Select] V01.00 x 105 m/s at 0 = 30° angle with respect to the plane, as shown in the figure below. Use the coordinate system in ✓? If the zero potential is the figure and neglect the effect of gravity. How high can the proton go [Select] at the origin level, i.e., y = 0 level, what is the potential energy [Select] height y21.00 m [Select] y [Select] 0 of the proton when it is at a height of y₁ = 0.500 m ? What is the proton's kinetic energy at Vo V 0 and kinetic energy Xarrow_forwardFind the Electric flux density D in the free space at point (2,0, n/2), if the potential V =- sin 0 sin Ø?.arrow_forward
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