The graphic illustrates the surface charge density of a disk that is uniformly charged and has an inner radius of a and an outer radius of b. What is the point P's electric potential? A. 2πko [√x² + b² − √x² + a²] x² + b² В. лko ln x²+a², С. пko [√x² + b² − x] D. 2πκσα In (x+√x²+b² √x+√x²+a² b

The graphic illustrates the surface charge density of a disk that is uniformly charged and has an inner radius of a and an outer radius of b. What is the point P's electric potential? A. 2πko [√x² + b² − √x² + a²] x² + b² В. лko ln x²+a², С. пko [√x² + b² − x] D. 2πκσα In (x+√x²+b² √x+√x²+a² b

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter26: Electric Potential

Section: Chapter Questions

Problem 42PQ: A line of charge with uniform charge density = 2.00 103 C/m lies along the x axis from x = 0.250 m...

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(a) Calculate the electric potential 0.250 cm from ail electron, (b) What is the electric potential difference between two points that are 0.250 cm and 0.750 cm from an electron? (c) How would the answers change if the electron were replaced with a proton?
Two parallel conducting plates, each of cross-sectional area 400 cm2, are 2.0 cm apart and uncharged. If 1.01012 electrons are transferred from one plate to the other, (a) what is the potential difference between the plates? (b) What is the potential difference between the positive plate and a point 1.25 cm from it that is between the plates?
An electron is at the origin, (a) Calculate the electric potential VA at point A, x = 0.250 cm. (b) Calculate the electric potential VB at point B, x = 0.750 cm. What is the potential difference VB VA? (c) Would a negatively charged particle placed at point A necessarily go through this same potential difference upon reaching point B? Explain.
In nuclear fission, a nucleus splits roughly in half, (a) What is the potential 2.001014 in from a fragment that has 46 protons in it? (b) What is the potential energy in MeV of a similarly charged fragment at this distance?
(a) What is the potential between two points situated 10 cm and 20 cm from a 3.0C point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?
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 very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of 3.00nC/m2 . (a) As the distance from the sheet increases, does the potential increase or decrease? Can you explain why without any calculations? Does the location of your reference point matter? (b) What is the shape of the equipotential surfaces? (c) What is the spacing between surfaces that differ by 1.00 V?
(a) Find the electric potential difference Ve required to stop an electron (called a stopping 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 of electric potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential. Vp/Ve.
A Consider a thin rod of total charge Q and length L (Fig. P26.43). Show that the electric potential at point P, a distance x from the end of the rod, is given by V(x)=kQLln(x+Lx) FIGURE P26.43 Problems 43 and 54.
In a certain region of space, the electric field is zero. From this fact, what can you conclude about the electric potential in this region? (a) It is zero, (b) It does not vary with position. (c) It is positive. (d) It is negative. (e) None of those answers is necessarily true.
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?
Two point charges, q1 = 2.0 C and q2 = 2.0 C, are placed on the x axis at x = 1.0 m and x = 1.0 m, respectively (Fig. P26.24). a. What are the electric potentials at the points P (0, 1.0 m) and R (2.0 m, 0)? b. Find the work done in moving a 1.0-C charge from P to R along a straight line joining the two points. c. Is there any path along which the work done in moving the charge from P to R is less than the value from part (b)? Explain.