Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.3, Problem 2.28P
To determine
The potential inside a uniformly charged solid sphere of radius R and total charge q.
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(4.58)
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An isolated solid spherical conductor of radius 5.00cm is surrounded by dry air. It is given a charge and acquires potential V, with the potential at infinity assumed to be zero.
a. Calculate the maximum magnitude can have.
b. Explain clearly and concisely why there is a maximum.
Problem 2.20 One of these is an impossible electrostatic field. Which one?
(a) Ek[xy x + 2yzý + 3xz2];
(b) E= k[y² + (2xy + z²) ŷ + 2yz 2].
Here k is a constant with the appropriate units. For the possible one, find the potential, 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 particular path
in mind.]
Problem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of
radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7.
Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose
radius is R and whose total charge is q. Use infinity as your reference point. Compute the
gradient of V in each region, and check that it yields the correct field. Sketch V (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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- Problem 4.19 Suppose you have enough linear dielectric material, of dielectric constant Er to half-fill a parallel-plate capacitor (Fig. 4.25). By what fraction is the capacitance increased when you distribute the material as in Fig. 4.25(a)? How about Fig. 4.25(b)? For a given potential difference V between the plates, find E, D, and P, in each region, and the free and bound charge on all surfaces, for both cases. Houminos ******************** qa (b)arrow_forwardProblem 2.20 One of these is an impossible electrostatic field. Which one? (a) E =k[xyÂ+2yzý+3xz2]; (b) E = k[y² + (2xy + z²)ý + 2yz 2). Here k is a constant with the appropriate units. For the possible one, find the potential, 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 particular path in mind.]arrow_forwardProblem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7. Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point. Compute the gradient of V in each region, and check that it yields the correct field. Sketch V(r).arrow_forward
- 1.20P) An infinite line charge with line charge density of 2 located near an infinite, grounded conducting plane as shown in figure. Find the potential everywhere. Draw electric field lines and show equipotential surfaces. Calculate E field at the conductor surface due to the surface charges of o. Clearly indicate that, is the electric field and potential at the boundary surfaces are continuous or not (Explain your reasoning). The question has a linear charge density at the position x = a, y = b. ラメarrow_forwardO [HW3.1] A solid metal ball (radius a) is grounded inside a floating (isolated) metal sphere (inner radius b, outer radius d). The sphere comes with total charge Q. Find surface charge density on every surface (the outer surface of the metal ball, inner and outer surface of the sphere), and capacitance of the system.arrow_forwardThis one is tougher! A sphere of radius r has charge q. (a) What is the infinitesimal increase in clectric potential energy dU if an infinitesimal amount of charge dq is brought to infinity to the surface of the sphere? (b) An uncharged sphere can acquire a total charge Q by the transfer of charge dq over and over and over. Use your answer to part a to find an cxpression for the potential energy of a uniformly-charged sphere of radius R with total charge Q. Answer: U = 3_1 Q² 5 4tc0 R' (c) Your answer to part b is the amount of energy nceded to assemble a charged sphere. It is often called the self-energy of the sphere. What is the self-energy of a proton, assuming it to be a charged sphere with a diamcter of 1.0 x 10 15 m?arrow_forward
- 6.10 The region between concentric spherical conducting shells r = 0.5 m and r = 1m is charge-free. If V(r = 0.5) = -50V and V(r =1) = 50 V, determine the potential dis- tribution and the electric field strength in the region between the shells.arrow_forwardI have the charge is d a charge o, riting at orizion- sumcounding Cubic bo z made of a perfect Conductor whose sides have length a. The domain of interest is volume Contained by box. a). Find expression of potential associated with this charge (This may be expression as sum). b). Find expression for surface charge density, one of inner walls of box (Again You can express this as sum). found onarrow_forward2.10 A large parallel plate capacitor is made up of two plane conducting sheets with separation D, one of which has a small hemispherical boss of radius a on its inner surface (D > a). The conductor with the boss is kept at zero potential, and the other conductor is at a potenti al such that far from the boss the electric field between the plates is Ep. (a) Calculate the surface-charge densities at an arbitrary point on the plane and on the boss, and sketch their behavior as a function of distance (or angle). (b) Show that the total charge on the boss has the magnitude 3mé, Ega?. (c) If, instead of the other conducting sheet at a different potential, a point charge q is placed directly above the hemispherical boss at a distance d from its center, show that the charge induced on the boss is d - a? q' = -q 1 dyd + a?arrow_forward
- function. 2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit length given by: Ao A(z) = { db e exp(-2/a) z≥0 x 0 are constants. Using spherical coordinates, find the electrostatic potential everywhere, assuming Þ(r → ∞) = 0. It is sufficient to express you answer in terms of definite integrals over r.arrow_forward4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. %3D (0, 5, 0)| PLA=A nC/m 20° z=0 plane (0, 3, 0) p= 3 PLB= 1.5 nC/m 10° 10° p=1.6 p= 3.5 Psc 1 nC/m2 20° FIGURE 4.11 See Prob. 20.arrow_forwardA right circular cylinder has an electrostatic potential of (p,4) on both ends. The potential on the curved cylindrical surface is zero. Find the potential at all interior points. 14.2.6 Hint. Choose your coordinate system and adjust your z dependence to exploit the symmetry of your potential.arrow_forward
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