Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.5, Problem 2.52P
(a))
To determine
The potential at any point
(b))
To determine
The radius of cylinder corresponding to given potential
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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)
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.
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 4.1I
The space between the plates of a parallel-plate capacitor (Fig. 4.24) is filled with
two slabs of linear dielectric material. Each slab has thickness a, so the total distance
between the plates is 2a. Slab-1 has dielectric constant of 2 and slab-2 has a dielectric
constant of 1.5. With the area of each of the top and bottom conducting plates is
much greater than a?, we can assume the the surface charge densities +o and -o on
the top and bottom plates is uniform.
(a) Find the electric displacement D in each slab.
(b) Find the electric field E in each slab.
(c) Find the potential difference between the plates.
(d) Find the locations and amounts of all bound charge.
(e) Based on the values of bound charge, recalculate E and verify your answer from
(b).
(f) How do your results relate to the formula for the addition of two series capacitors?
Chapter 2 Solutions
Introduction to Electrodynamics
Ch. 2.1 - (a) Twelve equal charges,q, arc situated at the...Ch. 2.1 - Find the electric field (magnitude and direction)...Ch. 2.1 - Find the electric field a distance z above one end...Ch. 2.1 - Prob. 2.4PCh. 2.1 - Prob. 2.5PCh. 2.1 - Find the electric field a distance z above the...Ch. 2.1 - Find the electric field a distance z from the...Ch. 2.2 - Use your result in Prob. 2.7 to find the field...Ch. 2.2 - Prob. 2.9PCh. 2.2 - Prob. 2.10P
Ch. 2.2 - Use Gauss’s law to find the electric field inside...Ch. 2.2 - Prob. 2.12PCh. 2.2 - Prob. 2.13PCh. 2.2 - Prob. 2.14PCh. 2.2 - A thick spherical shell carries charge density...Ch. 2.2 - A long coaxial cable (Fig. 2.26) carries a uniform...Ch. 2.2 - Prob. 2.17PCh. 2.2 - Prob. 2.18PCh. 2.2 - Prob. 2.19PCh. 2.3 - One of these is an impossible electrostatic field....Ch. 2.3 - Prob. 2.21PCh. 2.3 - Find the potential a distance s from an infinitely...Ch. 2.3 - Prob. 2.23PCh. 2.3 - Prob. 2.24PCh. 2.3 - Prob. 2.25PCh. 2.3 - Prob. 2.26PCh. 2.3 - Prob. 2.27PCh. 2.3 - Prob. 2.28PCh. 2.3 - Prob. 2.29PCh. 2.3 - Prob. 2.30PCh. 2.4 - Prob. 2.31PCh. 2.4 - Prob. 2.32PCh. 2.4 - Prob. 2.33PCh. 2.4 - Find the energy stored in a uniformly charged...Ch. 2.4 - Prob. 2.35PCh. 2.4 - Prob. 2.36PCh. 2.4 - Prob. 2.37PCh. 2.5 - A metal sphere of radius R, carrying charge q, is...Ch. 2.5 - Prob. 2.39PCh. 2.5 - Prob. 2.40PCh. 2.5 - Prob. 2.41PCh. 2.5 - Prob. 2.42PCh. 2.5 - Prob. 2.43PCh. 2.5 - Prob. 2.44PCh. 2.5 - Prob. 2.45PCh. 2.5 - If the electric field in some region is given (in...Ch. 2.5 - Prob. 2.47PCh. 2.5 - Prob. 2.48PCh. 2.5 - Prob. 2.49PCh. 2.5 - Prob. 2.50PCh. 2.5 - Prob. 2.51PCh. 2.5 - Prob. 2.52PCh. 2.5 - Prob. 2.53PCh. 2.5 - Prob. 2.54PCh. 2.5 - Prob. 2.55PCh. 2.5 - Prob. 2.56PCh. 2.5 - Prob. 2.57PCh. 2.5 - Prob. 2.58PCh. 2.5 - Prob. 2.59PCh. 2.5 - Prob. 2.60PCh. 2.5 - Prob. 2.61P
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- Problem 2.20 One of these is an impossible electrostatic field. Which one? (a) Ek[xy x + 2yzý + 3xz2]; (b) E= k[y² + (2xy + z²) ŷ + 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.] Problem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7. Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V (r).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. %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_forwardA coaxial cable consists of a copper wire, radius a surrounded by a concentric copper tube of inner radius c (Fig. 4.26). The space between the two conductors is partially filled (from radius b to radius c) with a linear dielectric material of dielectric constant Er. The gap from a to b has permittivity 6o. Find the capacitance per unit length of this cable.arrow_forward
- Consider a uniformly charged solid sphere of radius ? and total charge ? centered on the origin. In this problem you will calculate the potential ?(?) for ? < ? in two different ways. Use infinity as the reference point (i.e., ?(∞) = 0). (a) Use Eq. 2.21 of Griffiths to compute the potential at ? < ?. (b) Use Eq. 2.29 of Griffiths to compute the potential at ? < ?.arrow_forwardProblem 3.36 (3rd edition): Two long straight wires, carrying opposite uniform line charges +1, are situated on either side of a long conducting cylinder (Fig. 3.39). The cylinder (which carries no net charge) has radius R, and the wires are a distance "a" from the axis. Find the potential at point 7. (Hint: you can use solution of problem 2.47) R a aarrow_forward[ Q.3 A capacitor has orthogonal plates of length a and width b. The distance between the plates is h<< a, b. The capacitor has a charge Q. The space between the plates is initially vacuum and we insert slowly a slab of dielectric material as of dielectric constant & as shown in figure. What is the force that is exerted on the slab when it has entered a distance x inside the capacitor? aarrow_forward
- Consider the distribution of three charged particles as shown below. (a) What is the electric potential (voltage) at the point indicated with the dot (bottom right corner of the rectangle)? Express your answer in Volts. (b) If a proton were placed at the dot, and released from rest, what would be its speed very far away from these charges? Neglect air resistance and any gravitational forces.arrow_forwardProblem 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.]arrow_forwardAnswer All.Compute for the work done, in millijoules, in moving a 9-nC charge radially away from the center from a distance of 3 m to a distance of 7 m against the electric field inside a solid insulating sphere of radius 11 m and total charge 7 mC.Ans: -8.5199Determine the total potential energy, in microjoules, stored in a parallelepiped of dimensions are 9 m by 6 m by 8 m if the electric field inside is given as E = 17 ar + 19 aθ + 15 aϕ V/m. Use the permittivity of free space as 8.854 × 10-12 F/m.Ans: 1.6734If the electric field in the region is given as E = -cos(θ) sin( 4 Φ) aθ + b cos( 4 Φ) aφ V/m. Determine the potential at point A(4 m, 0.46 rad, 2.07 m), in volts, if the potential at point B(4 m, 1.00 rad, 0.10 m) is 60 volts. The value of b is also the coefficient of Φ.58.4552 Compute for the potential difference, in volts, in moving a charge from A(3, 2, -2) m to B(7, -6, 6) m against the electric field due to a disk charge of radius 9 m on the plane x = 0. The disk has a…arrow_forward
- Consider a solid cylindrical conductor of inner conductor radius 65 cm and outer conductor radius 77 cm with charge Q that is coaxial with a cylindrical shell of negligible thickness. Find the capacitance, in nF, of this cylindrical capacitor if its length is 61 m and the insulator used is mica (εr = 6).arrow_forwardO [HW3.1] A solid metal ball (radius a) is grounded inside a floating (isolated) metal sphere (inner radius b, outer radius d). The sphere comes with total charge Q. Find surface charge density on every surface (the outer surface of the metal ball, inner and outer surface of the sphere), and capacitance of the system.arrow_forward(a) Verify that F is a solenoidal vector field. (b) Find a vector potential G .arrow_forward
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