Question

An infinitely long solid cylindrical insulator of radius 13.0 cm has a non-uniform volume charge density of =4r3 where is in Cm3 when r is in meters. Calculate the magnitude of the electric field at a distance of 17.00 cm from the axis of the cylinder.

Answer 1

Electric field is asked outside the cylinder.

Let there be a gaussian cylinder of height H outside, at distance = 17cm

By Gauss Law,
Qenclosed by this gaussian cylinder / = E * 2r H [ r = 17cm ] ....1st equation
Qen = E * 2r H

To find Qen(this is the total charge inside the gaussian cylinder),
We take infinitely small cylindrical shells(at distance r,Height H ,thickness dr)of volume dV = 2r Hdr
Qen =

=

=

=

So,
Substituting in 1st equation
= E * 2r H
4 * (0.13 m )⁴ / 4 = E * 0.17 * [ r = 0.17 m ]

E = (0.13 )⁴ / 0.17 *

= 1.897 * 10⁸ N/C