Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Textbook Question
Chapter 4.4, Problem 4.21P
A certain coaxial cable consists of a copper wire, radius a, surrounded by a concentric copper tube of inner radius c (Fig. 4.26). The space betweenis partially filled (from b out toc) with material of dielectric constant
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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)
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
O
[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.
[
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?
a
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- 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?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_forwardProblem 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_forward
- Problem 4.19 Suppose you have enough linear dielectric material, of dielectric constant Er to half-fill a parallel-plate capacitor (Fig. 4.25). By what fraction is the capacitance increased when you distribute the material as in Fig. 4.25(a)? How about Fig. 4.25(b)? For a given potential difference V between the plates, find E, D, and P, in each region, and the free and bound charge on all surfaces, for both cases. Houminos ******************** qa (b)arrow_forwardConsider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to λ this line of charge is given by E= 2kef= -, where is a unit vector directed radially outward Σπερμ from the infinitely long wire of charge. Hint #3 a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to this infinite line of charge at some distance r from the line of charge. Give your answer in terms of given quantities (A,ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for V(r) calculation 3 V(r) = b. There is a reason we are not setting V(r → ∞o) = 0 as we normally do (in fact, in general, whenever you have an infinite charge distribution, this "universal reference" does not work; you need a localized charge distribution for this reference to work). Which of the following best describes what happens to potential as roo? (That is, what is V(ro), with our current…arrow_forwardFor problem 4 part b in square centimeters using inner and outer radii of the spherical capacitor of a = 2.00 cm and b = 1.05 a, respectively. (Answer in 5 sig. figs.)arrow_forward
- Consider 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_forwardProblem 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_forwardW = 'fD-Edr. (4.58)arrow_forward
- 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.]arrow_forwardConsider 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_forwardImagine that two parallel plates are charged to achieve a voltage difference Vo between the plates. They have area A and spacing d. The plates are then electrically isolated so that no charge can be added or taken away. A good conductor of thickness d/2 is placed in between the two plates, as shown. How great is the charge density on the surface of the conductor relative to that on either of the plates? Why? (You may use infinite plane approximations for the surfaces.)arrow_forward
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