Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Textbook Question
Chapter 2.1, Problem 2.7P
Find the electric field a distance z from the center of a spherical surfaceof radius R (Fig. 2.11) that carries a uniform charge density
in terms of R and
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Students have asked these similar questions
Problem 2.9Suppose the electric field in some region is found to be E = kr³î, in
spherical coordinates (k is some constant).
(a) Find the charge density p.
(b) Find the total charge contained in a sphere of radius R, centered at the origin.
(Do it two different ways.)
(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
sphere
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.
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.
b
WODY
1. Find the electric field for r
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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- Figure 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 using superposition.arrow_forwardProblem 2.7 Find the electric field a distance z from the center of a spherical surface of radius R (Fig. 2.11), which carries a uniform charge density o. Treat the case z R (outside). Express your answers in terms of the total charge q on the sphere. [Hint: Use the law of cosines to write r in terms of R and 0. Be sure to take the positive square root: VR? + z? - 2Rz = (R – z) if R > z, but it's (z – R) if R < z.]arrow_forwardA solid sphere of radius a, centered at the origin, carries a volume charge density of p(r) = ar², where a is a constant (see Fig. 2 below). a. Calculate the electric field inside and outside of the sphere. (NOTE: For a spherically symmetric system, dV = r² sin(e) de dødr. Therefore, the volume integral of some function p(r) is given by fp(r)r² sin(e) dedodr = 4n fp(r)r²dr) b. Plot the resulting electric field as a function of distance from the origin. aarrow_forward
- 2.6.1 Divergence Find hv.Edz, where E is the electric field due to a point charge q at x' and V is a sphere centered on the origin with radius b> |x'). please solve thisarrow_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_forwardA sphere of radius R has total charge Q. The volume charge density (C/m') within the sphere is p(r) = C/r² , where C is a constant to be determined. 1. Use the expression to find a magnitude of an electric field strenght E : a) inside the sphere (rarrow_forwardUsing the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0q)/( 242) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 2. ) We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E =…arrow_forwardA cylindrically symmetric charge distribution has charge density p(r) given by P()= 2na erla where Op and a are constants. Calculate the total charge O contained within a cylinder of length I = 5a and radius 2a, centred on the z-axis, and grve your answer by entering numbers in both of the boxes in the equation below: [Note that you must enter a value in each of the boxes, including 1 or 0 if appropriate. Blank boxes will be marked as incorrect.]arrow_forward1.13 Two infinite grounded parallel conducting planes are separated by a distance d. A point charge q is placed between the planes. Use the reciprocation theorem of Green to prove that the total induced charge on one of the planes is equal to (-q) times the fractional perpendicular distance of the point charge from the other plane. (Hint: As your comparison electrostatic problem with the same surfaces choose one whose charge densities and potential are known and simple.)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_forwardAn electric force is expressed as F = -pz sin o a, + p cos pa,. Transform F into cartesian coordinates and compute its magnitude at point (2,-1).arrow_forwardConsider a thin plastic rod bent into an arc of radius Rand angle a (see figure below). The rod carries a uniformly distributed negative charge Q -Q A IR What are the components and E, of the electric field at the origin? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the AE contributed by a representative piece. (b) Express algebraically the contribution each piece makes to the and y components of the electric field. Be sure to show your integration variable and its origin on your drawing. (Use the following as necessary: Q, R, cx, 0, A0, and EQ-) ΔΕ, = - TE aR² AB=(2 Lower limit= 0 ✓ e aR² Upper limit= a X cos(0)40 x (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. sin (0)40 x Evaluate the integral. (Use the following as necessary: Q, R, a, and E.) Editarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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