Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.2, Problem 2.12P
To determine
The electric field inside a uniformly charged solid sphere having volume charge density
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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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- An infinitely long cylindrical conductor of a radius r is charged with a uniformly distributed electrical charge, if the charge per unit length of it equal A coulomb/m. ( using gauss law) calculate the electric field at point d. d.arrow_forwardA part of a Gaussian Surface is a square of side length s. A corner of the square is placed the distances from the origin on the y axis. A point charge Q is located at the origin. The edges of the square are either parallel to the x direction or z direction. The image above shows this information. If Q=25 microCoulomb and s= 15 cm, what is the electric field flux through the square? O none of these O 2.82 106 Nm²/C O 7.06 105 Nm²/C O 1.18 105 Nm²/C O 4.71 105 N*m²/Carrow_forwardELECTROMAGTNETICS: Electric Flux Density and Divergence Theorem Solve the following problems accordingly. Show your solution. Using left side of the divergence theorem, find the total charge enclosed in the rectangular parallelepiped 0 < x < 2,0 < y < 3,0 < z < 5 cm. Let D = 4xy ax + 2(x? + z?)a, + 4yza, nC/m².arrow_forward
- Please fill in the blanks. (Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol. Using Gauss Law...)arrow_forwardA very long, uniformly charged cylinder has radius R and volumetric charge density \rho. Find the cylinder's electric field for: a.) outside the cylinder, r> = Rb.) inside the cylinder, r < = Rc.) Show that your answers to parts (a) and (b) match at the boundary r = Rarrow_forwardA plane with a circular hole of radius R is uniformly charged with areal density o. Find the strength E of the electric field on the axis of the hole as a function of the distance h to its center. Hint: Use the principle of wwwmm superposition.arrow_forward
- We have said that Gauss's law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. a) Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss's law to find the field of a sphere whose density depends on distance r from the center? Can we do it for a sphere whose density depends on angle (e.g. different at the poles from at the equator)? Why or why not? b) Can we use it for a uniformly charged ring? a uniformly charged cube? Why or why not? c) Summarize the key features for each of the possible distributions when the charge density is uniform throughout the sphere, cylinder or plate by filling out the table below answering the following questions: What is the shape of the test surface? What variable do we (or the text) usually use to indicate…arrow_forwardFind the electric field everywhere of an infinite uniform line charge with total charge Q. Sol. Using Gauss's Law: /EO EA = Eo Since, its the line charge we use the area of a cylinder surrounding the line charge E*2 L= But all the charged get enclosed by the cylinder area, so Cenc =Q Deriving we get: E= (1/2 TEO 1 IrL)arrow_forwardThe figure below shows a very long, thick rod with radius R, uniformly charged throughout. Find an expression for the electric field inside the rod (r< R). (Use the following as necessary: r, R, λ for the linear charge density of the rod, and o.) = Z Use the equation, 1 2πεο r to check your solution at the surface, where r = R. (Use the following as necessary: R, λ, and εo.) E(r = R) = = R ↑ 1 7arrow_forward
- Find the electric field (magnitude and direction) a distance z above the center of a circular loop or radius r that carries a uniform surface charge sigma. What does the formula give when r -> infinity? What happens when z>>r?arrow_forwardvt . A line of positive charge is formed into a semicircle of radius R as shown in the fig- ure to the right. The charge per unit length along the semicircle is given by A, and is constant. The total charge on the semicir- cle is Q. R (a) Determine the constant, A, in terms of the Coulomb constant k, total charge Q, and radius R. (b) What is the electric ficld, E (magnitude and direction), at the origin (the center of curvature)? Note: Recall that the arclength subtended by an angle 0 in radians along a circle of radius R is s = R0. Furthermore, you might find the following integral useful: "T/2 cos 0 do = 2. T/2arrow_forwardAs4 A coaxial cable of infinite length with an inner conductor a wrapped around it by a thin conductive sheet of radius b. The charge on the inner conductor has a distribution uniform p. The outer conductor is grounded. Calculate the electric field at any point (r < a,a < r < r and b > b)arrow_forward
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