11) A thin rod extends along the x-axis from x = −a to x = a . The rod carries a positive charge +Q uniformly distributed along its length 2a with charge density λ, as shown in Figure 7. • a) Use dV = 1/4πε0 ∫dq/r to show that the electric potential at point P is given by V (x) = (λ/4πε0) ln (x + a/x − a) • b) What is the electric potential of the rod at x = 4a and x = 2a? • c) What is the electric potential difference between x = 4a and x = 2a? • d) Now consider that there is an electron moving from x = 4a to x = 2a. What is the change in the electrostatic potential energy (∆U) of the electron? (calculate it in terms of the parameters defined in the problem) • e) Explain the reason why ∆U in part d is positive or negative.
11) A thin rod extends along the x-axis from x = −a to x = a . The rod carries a positive charge +Q uniformly distributed along its length 2a with charge density λ, as shown in Figure 7. • a) Use dV = 1/4πε0 ∫dq/r to show that the electric potential at point P is given by V (x) = (λ/4πε0) ln (x + a/x − a) • b) What is the electric potential of the rod at x = 4a and x = 2a? • c) What is the electric potential difference between x = 4a and x = 2a? • d) Now consider that there is an electron moving from x = 4a to x = 2a. What is the change in the electrostatic potential energy (∆U) of the electron? (calculate it in terms of the parameters defined in the problem) • e) Explain the reason why ∆U in part d is positive or negative.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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11) A thin rod extends along the x-axis from x = −a to x = a . The rod carries a positive charge +Q uniformly
distributed along its length 2a with charge density λ, as shown in Figure 7.
• a) Use dV = 1/4πε0 ∫dq/r to show that the electric potential at point P is given by
V (x) = (λ/4πε0) ln (x + a/x − a)
• b) What is the electric potential of the rod at x = 4a and x = 2a?
• c) What is the electric potential difference between x = 4a and x = 2a?
• d) Now consider that there is an electron moving from x = 4a to x = 2a. What is the change in the
electrostatic potential energy (∆U) of the electron? (calculate it in terms of the parameters defined in the
problem)
• e) Explain the reason why ∆U in part d is positive or negative.
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