A rod of length L is lying on x-axis with left end at the origin and has a non-uniformly linear charge density of 2 = 5x.. 22. find the electric potential V at A(-4, 0) Hint: dv= KdE dz = 2dx (-4,0) + + + 4 4 ¢ t + t A

A rod of length L is lying on x-axis with left end at the origin and has a non-uniformly linear charge density of 2 = 5x.. 22. find the electric potential V at A(-4, 0) Hint: dv= KdE dz = 2dx (-4,0) + + + 4 4 ¢ t + t A

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 44PQ: Figure P26.44 shows a rod of length = 1.00 m aligned with the y axis and oriented so that its lower...

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(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.
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.
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.
In a certain region of space, a uniform electric field is in the x direction. A particle with negative charge is carried from x = 20.0 cm to x = 60.0 cm. (i) Does the electric potential energy of the charge-field system (a) increase, (b) remain constant, (c) decrease, or (d) change unpredictably? (ii) Has the particle moved to a position where the electric potential is (a) higher than before, (b) unchanged, (c) lower than before, or (d) unpredictable?
A source consists of three charged particles located at the vertices of a square (Fig. P26.32), where the square has sides of length 0.243 m. The charges are q1 = 35.0 nC, q2 = 65.0 nC, and q3 = 56.5 nC. Find the electric potential at point A located at the fourth vertex. FIGURE P26.32 Problems 32 and 33.
A charged particle is moved in a uniform electric field between two points, A and B, as depicted in Figure P26.65. Does the change in the electric potential or the change in the electric potential energy of the particle depend on the sign of the charged particle? Consider the movement of the particle from A to B, and vice versa, and determine the signs of the electric potential and the electric potential energy in each possible scenario.
An infinite number of charges with |q| =2.0 C are placed along the x axis at x = 1.0 m, x = 2.0 m, x = 4.0 m, x = 8.0 m, and so on, as shown in Figure R26.79. What will be the electric potential at x = 0 if the consecutive charges have alternating signs as shown in Figure P26.79? Hint: Use the mathematical formula for a geometric series, 1+r+r2+r3+r4+=11r FIGURE P26.79
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.
Two 5.00-nC charged particles are in a uniform electric field with a magnitude of 625 N/C. Each of the particles is moved from point A to point B along two different paths, labeled in Figure P26.65. a. Given the dimensions in the figure, what is the change in the electric potential experienced by the particle that is moved along path 1 (black)? b. What is the change in the electric potential experienced by the particle that is moved along path 2 (red)? c. Is there a path between the points A and B for which the change in the electric potential is different from your answers to parts (a) and (b)? Explain. FIGURE P26.65 Problems 65, 66, and 67.
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.
(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) 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.