Problem 2: A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder? a) Compute the surface charge density n of the shell from its total charge and geometrical parameters. Vcenter = 1 Q b) Which charge dq is enclosed in a thin ring of width dz located at a distance z from the center of the cylinder (shown in Fig.2)? Which potential dV does this ring create at the center (you need to use the formula derived in the textbook for the potential of a charged ring along its axis). 4περ L dz R O O c) Sum up the contributions from all the rings along the cylinder by integrating dV with respect to z. Show that In √√R² + ² + 4 L √√R² +4² - 4/1 L FIG. 2: The scheme for Problem 2 & V dt (The integral that you need to use here is ²² = In (t + √t² + a²) ².)

Problem 2: A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder? a) Compute the surface charge density n of the shell from its total charge and geometrical parameters. Vcenter = 1 Q b) Which charge dq is enclosed in a thin ring of width dz located at a distance z from the center of the cylinder (shown in Fig.2)? Which potential dV does this ring create at the center (you need to use the formula derived in the textbook for the potential of a charged ring along its axis). 4περ L dz R O O c) Sum up the contributions from all the rings along the cylinder by integrating dV with respect to z. Show that In √√R² + ² + 4 L √√R² +4² - 4/1 L FIG. 2: The scheme for Problem 2 & V dt (The integral that you need to use here is ²² = In (t + √t² + a²) ².)

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 86AP: Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2...

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