The electric potential inside a charged spherical conductor of radius R is given by V = keQ/R, and the potential outside is given by V = keQ/r. Using E, = -dV/dr,derive the electric field inside and outside this charge distribution. (Use the following as necessary: ke, Q, r and R.)(a) insideE =(b) outsideE =

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Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 22P

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The electric potential inside a charged spherical conductor of radius R is given by V = keQ/R, and the potential outside is given by V = keQ/R, Using Er = dV/dr, derive the electric field (a) inside and (b) outside this charge distribution.
The charge density on a disk of radius R = 12.0 cm is given by = ar, with a = 1.40 C/m3 and r measured radially outward from the origin (Fig. P26.45). What is the electric potential at point A, a distance of 40.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration.
A filament running along the x axis from the origin to x = 80.0 cm carries electric charge with uniform density. At the point P with coordinates (x = 80.0 cm, y = 80.0 cm), this filament creates electric potential 100 V. Now we add another filament along the y axis, running from the origin to y = 80.0 cm, carrying the same amount of charge with the same uniform density. At the same point P, is the electric potential created by the pair of filaments (a) greater than 200 V, (b) 200 V, (c) 100 V, (d) between 0 and 200 V, or (e) 0?
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A metallic sphere of radius 2.0 cm is charged with +5.0C charge, which spreads on the surface of the sphere uniformly. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius 5.0 cm and outer radius 6.0 cm. Now, a charge of 5.0C is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. If potential is zero at infinity, what is the potential of (a) the spherical shell, (b) the sphere, (c) the space between the two, (d) inside the sphere, and (e) outside the shell?
(a) Find the potential difference VB required to stop an electron (called a slopping potential) moving with an initial speed of 2.85 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, Vp/Ve. The answer should be in terms of the proton mass mp and electron mass me.
A small spherical pith ball of radius 0.50 cm is painted with a silver paint and then -10 C of charge is placed on it. The charged pith ball is put at the center of a gold spherical shell of inner radius 2.0 cm and outer radius 2.2 cm. (a) Find the electric potential of the gold shell with respect to zero potential at infinity, (b) How much charge should you put on the gold shell if you want to make its potential 100 V?
An election enters a region between two large parallel plates made of aluminum separated by a distance of 2.0 cm and kept at a potential difference of 200 V. The electron enters through a small hole in the negative plate and moves toward the positive plate. At the time the electron is near the negative plate, its speed is 4.0103 m/s. Assume the electric field between the plates to be uniform, and find the speed of electron at (a) 0.10 cm, (b) 0.50 cm, (c) 1.0 cm, and (d) 1.5 cm from the negative plate, and (e) immediately before it hits the positive plate.
(a) Find the potential difference VB required to stop an electron (called a slopping potential) moving with an initial speed of 2.85 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, Vp/Ve. The answer should be in terms of the proton mass mp and electron mass me.
Show that electric potential for a shell whose radius is R, has charge q uniformly distributed on its entire surface, is the same as electric potential for a conductor (Solid) has radius R and charge q.
Consider a thick insulating spherical shell of a uniform volume charge density with a total charge Q = 6 Mu-C, an inner radius a = 10 mm, and an outer radius b = 60 mm. Find the electric potential for r = 55 mm.
What is the absolute potential at each of the following distances of 2.0 μC: r = 10 cm and r = 50 cm?

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nductor of radius R is given by V = keQ/R, and the rge distribution. (Use the following as necessary: k