Question

Shown in the figure below is an infinitely long solid cylinder of charge. The radius of the cylinder is a and the charge density is p. There are two regions indicated in the figure and you will find the electric field in each of these two regions. Region I (ra) Region II (rca) Infinite Solid Cylinder with Charge Density Region I: (outside the cylinder, r>) . What is the formula for the USEFUL area of the Gaussion surtec? A-2RL What is the formula for the charge inside? Opral X • What is the formula for the electric field? X Region 11: (inside the cylinder, r<a) • What is the formula for the USEFUL area of the Gaussian surface? A 2xPL • What is the formula for the charge nude? O.- LP X • What is the formula for the electric field? pr 20 NOTE: • Use and Pin your . Do not knor in your res • Use the "how variable in your son surface and responses • The USEFUL wes of the Gaussian surface is the portion for which z. o rotero

Answer 1

1) For the area of gaussian surface you are right but mistakenly ypu have written R instead of r

so $A=2\pi rL$

3) So electric field is also you can ca;culate from gauss law

as

Qenc ρίπα?L) Ε(2πχL) = = EO ED

so

$E=\frac{\rho a^2}{2r\epsilon_0}$

5) Now charge enclosed by cylinder inside r<a is then given by

$Q=\rho V=\rho \pi r^2 L$