By integrating the electric field as in Eq. (23.17), find the potential at a distance r from a point charge q. IDENTIFY and SET UP We let point a in Eq. (23.17) be at distance r and let point b be at infinity (Fig. 23.14). As usual, we choose the potential to be zero at an infinite distance from the charge q. EXECUTE To carry out the integral, we can choose any path we like be- tween points a and b. The most convenient path is a radial line as shown in Fig. 23.14, so that dl is in the radial direction and has magnitude dr. Writing di = fdr, we have from Eq. (23.17) de= direction V - 0 = V = E; di 2 L rdr dr 4TEor = 0 4TEor, 4TEor, 4TEor

By integrating the electric field as in Eq. (23.17), find the potential at a distance r from a point charge q. IDENTIFY and SET UP We let point a in Eq. (23.17) be at distance r and let point b be at infinity (Fig. 23.14). As usual, we choose the potential to be zero at an infinite distance from the charge q. EXECUTE To carry out the integral, we can choose any path we like be- tween points a and b. The most convenient path is a radial line as shown in Fig. 23.14, so that dl is in the radial direction and has magnitude dr. Writing di = fdr, we have from Eq. (23.17) de= direction V - 0 = V = E; di 2 L rdr dr 4TEor = 0 4TEor, 4TEor, 4TEor

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 82P

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