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Solved: A very long, solid cylinder with radius R has
Chapter 22, Problem 42P(choose chapter or problem)
Problem 42P
A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume ρ. (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 ρ. (b) What is the electric field at a point outside the volume in terms of the charge per unit length λ 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:
Problem 42P
A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume ρ. (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 ρ. (b) What is the electric field at a point outside the volume in terms of the charge per unit length λ 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 42P
Step 1:
Introduction :
In this question, we need to derive an expression for electric field inside the volume at distance r from the axis of the cylinder in terms of charge density
In the second part, we need to find the electric field at a point outside the volume in terms of
In the third part , we need to compare the answers to part 1 and 2 for r=R
And finally we need to draw a graph for electric field magnitude as function of r=0 to r=3R