A hollow, thin-walled insulating cylinder of radius R  and length L (like the cardboard tube in a roll of toilet paper) has charge Q  uniformly distributed over its surface. Part A Calculate the electric potential at any point x along the axis of the tube. Take the origin to be at the center of the tube, and take the potential to be zero at infinity. Express your answer in terms of the given quantities and appropriate constants.  Part B Use the result of part A to find the electric field at any point x along the axis of the tube. Express your answer in terms of the given quantities and appropriate constants.

Project 7 Consider an air-filled coaxial cable with conductors of square cross section, as shown in figure below. Let the 2D cross-sectional dimensions of the cable be a and b (a > b). The cable gets charged through static charges, and potential of the conductors are Vo and 0. Visualize and sketch the electric potential V distribution betrween the two conductors (contour plot) and electric flux lines distribution. Vo

Imagine the spherical equipotential surfaces of a positive point charge as illustrated. A positive test charge q0=1.00×10−9 C is brought from X to Y, and then to Z. Determine the total work done by the electric field in moving the test charge. Show all solutions.

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The charge density on a disk of radius R = 11.6 cm is given by o = ar, with a = 1.46 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 44.0 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. V R A

Problem 1: A spherical conductor is known to have a radius and a total charge of 10 cm and 20uC. If points A and B are 15 cm and 5 cm from the center of the conductor, respectively. If a test charge, q = 25mC, is to be moved from A to B, determine the following: d. The rate of change of the potential with respect to length or displacement in the conductor

The charge density on a disk of radius R = 11.2 cm is given by o = ar, with a = 1.30 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 30.0 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. R A A

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The potential of a thin spherical shell of radius R is given as V(R, 0) = 3 cos² 0 + cos 0 - 1. Both inside and outside the sphere, there is empty space with no charge density. The questions on this page are based on this system. What is the linear combination of the two Legendre polynomials that will generate this potential (Denote a Legendre Polynomial as P₁, where I is the index of the polynomial starting from 1 = 0)? O a. 2P₁ + P₂ O b. 2P3 + P₁ O c. Po + P₁ O d. None of the listed answers. O e. 2P₂ + P1₁ Of. P3 + P2 What is the radial part of the potential V(r, 0) inside the spherical shell for the Pi with the lowest l (i.e. the pre-factor of Pi)? O a. r O b. None of the listed options. O c. r/R O d. 2 O e. O f. (r/R)² 1/²