Solution Found!
(a) From the expression for E obtained in problem find the
Chapter 23, Problem 69P(choose chapter or problem)
(a) From the expression for E obtained in problem find the expressions for the electric potential V as a function of r, both inside and outside the cylinder. Let V = 0 at the surface of the cylinder. In each case, express your result in terms of the charge per unit length ? of the charge distribution. (b) Graph V and E as functions of from r = 0 to r = 3R. Problem: A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density ?. (b) What is the electric field at a point outside the volume in terms of the charge per unit length ? in the cylinder? (c) Compare the answers to parts (a) and (b) for r = R. (d) Graph the electric-field magnitude as a function of r from r = 0 to r = 3R.
Questions & Answers
QUESTION:
(a) From the expression for E obtained in problem find the expressions for the electric potential V as a function of r, both inside and outside the cylinder. Let V = 0 at the surface of the cylinder. In each case, express your result in terms of the charge per unit length ? of the charge distribution. (b) Graph V and E as functions of from r = 0 to r = 3R. Problem: A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density ?. (b) What is the electric field at a point outside the volume in terms of the charge per unit length ? in the cylinder? (c) Compare the answers to parts (a) and (b) for r = R. (d) Graph the electric-field magnitude as a function of r from r = 0 to r = 3R.
ANSWER:Solution 69P Let us solve the second question first to arrive at the electric field magnitudes inside and outside the volume. Charge per unit volume is given as . 2 The volume of the cylinder is = R l, where l is the length of the cylinder. Inside the volume r < R, Charge = r l 2 Applying G