Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Textbook Question
Chapter 3.4, Problem 3.35P
A solid sphere, radius R, is centered at the origin. The “northern”hemisphere carries a uniform charge density
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A thin glass rod is bent into a semicircle of radius R. A charge +Q is uniformly distributedalong the upper half, and a charge –Q is uniformly distributed along the lower half as shown in the figure. Find the magnitude and direction of the electric field E (in component form) at point P, the center of the semicircle.
QUESTION 7
Prob.2. An excess positive charge Q is uniformly distributed throughout the volume of an
insulating solid sphere of radius R = 4.0cm. The magnitude of the E-field at point P, 8.0cm from
the center of the sphere is given to be 4.5x107N/C.
What is the magnitude of the E-field ( in units of 10°N/C) at the surface of the sphere?
(Example: If your answer is 2.3x10'N/C, enter your answer as 23 in the answer box).
Problem 3: UP 6.53
Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume
of radius R. Show that the field of this charge distribution is directed radially with respect to the
cylinder and that
E(s) =
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2€0
PR²
2€ S
S≤R
SZR
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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- A uniformly charged conducting plate with area A has a total charge Q which is positive. Consider a cross-sectional view of the plane and the electric field lines due to the charge on the plane. +Q E E P Find the magnitude of the field at point P, which is a distance a from the plate. Assume that a is very small when compared to the dimensions of the plate, such that edge effects can be ignored.arrow_forwardFind the ratio of q/Q for the E-field to be zero at adistance of z = 3.52R for the charge distributionand geometry of problem #30 of the text. a isthe charge on the LARGER ring. Q is the chargeon the SMALLER ring.arrow_forwardA uniformly charged solid spherical insulator has a radius of 0.25 m. The total charge in the volume is 3.5 pC. Find the E-field at the position of 0.14 m from the center of the sphere.arrow_forward
- A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.arrow_forwardconsider a spherical shell with inner radius R1=0.40m and outer radius R2=1.1m. the hollow insider the shell contains no charge; and charge is distributed on the inside surface of the shell and within the shell itself. such that the electrical field inside the shell itself is everywhere outward pointing and of uniform constant magnitude 40 N/C What is the charge per unit volume at radius r=0.55m(within the material of the shell). Thanksarrow_forwardA spherical shell of radius R carries charge Q uniformly distributed over its surface. Suppose there is a tiny gap dividing the sphere in two equal halves. Find the force of repulsion between these two halves.arrow_forward
- consider a spherical shell with inner radius R1=0.40m and outer radius R2=1.1m. the hollow insider the shell contains no charge; and charge is distributed on the inside surface of the shell and within the shell itself. such that the electrical field inside the shell itself is everywhere outward pointing and of uniform constant magnitude 40 N/C What is the charge per unit volume at radius r=0.55m(within the material of the shell). 1.93e-9 and 3.14e-9 are both wrong answers. Pls kindly help to provide another answer Thanksarrow_forwardSuppose a piece of infinite length. We have the surface density of Sigma, which has width a, find the field at distance z؟arrow_forwardConsider a right triangle ABC with the right triangle at vertex B. The charges at A, at B, and at C, are known to be 5 mC, 4 mC, and 7 mC, respectively. Given that the side AB is 9 meters, and AC is thrice AB, find the magnitudes of the force and of the electric field at B.arrow_forward
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