Try the fastest way to create flashcards
Question

An extremely long, solid nonconducting cylinder has a radius $R_0$. The charge density within the cylinder is a function of the distance $R$ from the axis, given by $\rho_{\mathrm{E}}(R)=\rho_0\left(R / R_0\right)^2$. What is the electric field everywhere inside and outside the cylinder (far away from the ends) in terms of $\rho_0$ and $R_0$ ?

Solution

Verified
Step 1
1 of 5

Suppose we have a very long non conducting cylinder, with radius of $R_0$ and charge density of $\rho_E(R)=\rho_0 \left(\frac{R}{R_0}\right)^2$, we need to find the electric field inside and out side the cylinder, first, inside the cylinder, draw a Gauss surface (cylinder) inside the original cylinder with radius of $R$ and length of $l$ as shown in the following figure:

Recommended textbook solutions

Physics for Scientists and Engineers with Modern Physics

4th EditionISBN: 9780131495081 (8 more)Douglas C Giancoli
7,069 solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions

Introduction to Electrodynamics

4th EditionISBN: 9780321856562 (3 more)David J. Griffiths
956 solutions

Introduction to Quantum Mechanics

3rd EditionISBN: 9781107189638Darrell F. Schroeter, David J. Griffiths
485 solutions