Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.5, Problem 2.58P
(a)
To determine
Three other points inside the triangle where the electric field is zero.
(b)
To determine
The distance from the center the
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Consider n equal positively charged particles each of magnitude Q/n placed symmetrically around a circle of radius a. Calculate the magnitude of the electric field at a point a distance x from the center of the circle and on the line passing through the center and perpendicular to the plane of the circle. (Use any variable or symbol stated above along with the following as necessary: ke.)
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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- (a) Consider a uniformly charged thin-walled right circular cylindrical shell having total charge Q, radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the figure below. Suggestion: Use the following expression and treat the cylinder as a collection of ring charges. (Use any variable or symbol stated above along with the following as necessary: ke.) E = кех (x² + a²j3/20 E = R (b) Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the following expression to find the field it creates at the same point. (Use any variable or symbol stated above along with the following as necessary: k.) X 2xk, 0 (1 - (2²+42²271/72) 2лk darrow_forwardGiven that D = 10 x 3 3 a x(μC/m2), determine the total charge (in microcoulombs) enclosed in a cube of 2 m on an edge, centered at the origin and with edges parallel to the axes.arrow_forwardAn infinite plane slab, of thickness 2d, carries a uniform volume charge density (rho). Find the electric field, as a function of y, where y = 0 at the center. Plot E versus y, calling E positive when it points in the +y direction and negative when it points in the −y direction.arrow_forward
- (1) In this problem, we will calculate the electric field of a line charge. The line charge is aligned along the x-axis starting at the origin and having a length L. The line has a linear charge density ). We want to find the electric field at a point P at the point (d,0). (a) What is the charge dq in terms of the given parameters and coordinates? (b) What is the distance between an arbitrary point on our line charge to the point P in terms of given parameters and coordinates (|r])? (c) What is the unit vector î in terms of given parameters and coordinates? (d) What is the electric field of this line charge in terms of given parameters and coordi- nates?arrow_forwardA circular disk of radius a (lies on z = 0) is uniformly charged with rhos C/m^2. (A) Find the electric field E at (0,0,h). (B) Find E at (0,0,0) and (0,0,infinity) based on the result of part (A). The answer to part (A) is E = (\rhos / 2*permitivity of free space)(1 - (h / ((a^2 + h^2)^1/2)))az. Please provide a detailed step-by-step solution to part (B). Thank you!arrow_forwardWe will continue the analysis of the electric dipole starting from part d of problem 1, but in the long-distance limit. It will be convenient to use the distance, r, from the origin, r = angle 0 between and the z axis: Vx2 + z2 and the z = r cos 0, x = r sin 0. The long-distance limit corresponds to r >> d. In the denominator of your result from problem 1 part d, you will have terms that look like Vx2 + (z ± d/2)². Rewrite those in terms of r and r cos e and factor out an r2 from each of the terms inside the radical. Then pull that r² out of the square root leaving an expression inside the quadratic that is amenable to a binomial approximation. However, we will only keep terms to first power in d/r so you will want to drop a term inside each square root before applying the binomial approximation. Apply the binomial approximation to the two terms you obtained from problem 1d and combine them. Show that the electric field in the long-distance limit can be written 1 qd (1) 4m€0 r3 (3 cos…arrow_forward
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