Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.1, Problem 2.5P
To determine
To find:The electric field at z distance away from the center of the circular loop.
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A point charge +Q is placed at the centre
of an uncharged spherical conducting shell of inner radius
a and outer radius b as shown in Fig. 2.51.
Fig.
53
b.
~
1. Find the electric field for r
(b) A smaller metal sphere, also mounted on an insulating plastic stand, is uncharged.
This smaller sphere is moved close to the positively charged sphere. Fig. 1.1 shows the two
spheres.
positively
charged
sphere
I-I
smaller
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plastic
stands
Fig. 1.1
(i) On Fig. 1.1, draw the distribution of charge on the smaller sphere.
(ii) An earthed metal wire is touched against the smaller metal sphere.
Štate and explain what happens to the charge on the smaller sphere.
(c) Explain, in terms of their structures, why the metal wire is an electrical conductor but the
plastic stand is an electrical insulator.
Two identical He-filled spherical bal-
loons each carrying a charge q are tied to a weight W with
strings and float in equilibrium as shown in Fig. 1.12(a).
Find:
1. the magnitude of q, assuming that the charge on each
balloon acts as if it were concentrated at the centre.
2. the volume of each balloon.
9, m
(8)
W
q, m
Fig.
mg
T cose
T sine
(b)
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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- Two identical He-filled spherical bal. loons each carrying a charge q are tied to a weight Wwith strings and float in equilibrium as shown in Fig. 1.12(a). Find: 1. the magnitude of q, assuming that the charge on each balloon acts as if it were concentrated at the centre. 2. the volume of each balloon. 9, m (8) q, m Fig. mg T cose T sine (b)arrow_forwardTwo identical He-filled spherical bal- loons each carrying a charge q are tied to a welght Wwith strings and float in equilibrium as shown in Fig. 1.12(a). Find: 1. the magnitude of 4, assuming that the charge on each balloon acts as if it were concentrated at the centre. 2. the volume of each balloon. 9, m 818 (a) 1 W q, m Fig. F← mg B T cose T T sin (b)arrow_forwardFigure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise in three ways: a) direct integration, b) by superposition, and c) using the relationship for a force on a small patch.arrow_forward
- 2.12 Use Gauss' law to determine the E field produced by a spherical charge distribution of density p = a/r2, where a is a constant.arrow_forwardProblem 2.01. Three plates with surface charge density |o| = 8.85 μC/mm² are stacked on top of each other. The top and bottom plates have charge density to while the center plate has charge density -0. (a) Find the magnitude and direction of the electric field between the plates. (b) Find the magnitude and direction of the electric field above and below the plate stack.arrow_forwardI have parts A & B. I just need help with c. The figure is attached. For the cylinder of uniform charge density in Fig. 2.26: (a) show that the expression there given for the field inside the cylinder follows from Gauss’s law My Answer: p = rho r<a: E = (p*r)/ (2 * epsilon not) r>a: E = (p * a^2)/(2 * epsilon * r) (b) find the potential φ as a function of r, both inside and outside the cylinder, taking φ = 0 at r = 0. My Answer: r<a: φ(r) = (-p * r^2)/(4 * epsilon not) r>a: φ(r) = (-p * a^2)/(4 * epsilon not) - (p * a^2)/(2 * epsilon not)(In(r/a)) c) Take the Laplacian in cylindrical coordinates and show that Poisson’s equation holds in this example.arrow_forward
- Problem 2.20 One of these is an impossible electrostatic field. Which one? (a) E= k[xy x + 2yz y + 3xz 2]; (b) E= k[y² + (2xy + z²)ŷ + 2yz2]. Here k is a constant with the appropriate units. For the possible one, find the poten- tial, 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 definite path in mind.]arrow_forward5.1.A spherical conductor has a spherical cavity with the same center point.at the center of the cavity there is a point charge of q. If a total charge of Q is placed on the conductor ,what is Q i ,the total charge on the inner surface of the conductor? 2. Q o,the total charge on the outer surface of the conductor? 3.If the cavity has a radius of a and the conductor has a radius of b,what is the surface charge density on the inner surface of the conductor? 4.The outer surface of the conductor? 5.Assume that the charges on the inner and outer surface are uniformly distributed.Draw the electric field lines on the diagramarrow_forwardAn insulating solid sphere of radius 3 m has 15 C of charge uniformly distributed throughout its volume. Calculate the charge contained in a Gaussian surface having a radius 1/2 that of the sphere. Present your answer accurately to 2 decimal numbers i.e 3.20. Do not include units!arrow_forward
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