Question

Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 1.00×10^-2m. The charge density is 4.00×10^-2C/ m³. What is the electric field at r = 5.00×10^-3m?

What is the electric field at r = 2.00×10^-2m?

Answer 1

Radius of the cylinder   r = 1.00x10^-2 m , eps₀ = 8.854x10^-12

Charge density row = 4.00x10^-2 C/m³

Here the charge density is continous and distributed over the whole volume of the Cylinder.

By Gauss law,

        Surface indegral of E . da = volume integral of row x dv

                       E x 2 pi x r x h = row/eps₀ x pi x r² x h

a) Inside the Cylinder, r < R

                      E = row x r / 2 x eps₀

        r = 5.00 x10^-3 m

                  E = 4.00x10^-2 x 5.00x10^-3 / ( 2 x 8.854x10^-12)

                       E = 1.129x10⁷ N/C

b) Ouside the cylinder, r > R

                        E = row x R² / 2 eps₀ r

                            = 4.00x10^-2 x (1.00x10^-2 )² / ( 2 x 8.854x10^-12 x 2.00x10^-2 )

                              E = 1.129x10⁵ N/C