Question

A very long solid insulating cylinder has radius R = 0.1 m and uniform charge density rho0= 10-3 C/m3. Find the electric field at distance r from the axis inside the cylinder in terms of r/R.​

Answer 1

`E = (0.56 * 10^8 ) r \ \ N/c`

Step-by-step explanation:

Given that:

`\rho_o = (10^(-3) ) \ c/m^3`

R = (0.1) m

To find the electric field for r < R by using Gauss Law

`{\oint}E^(\to)* da^(\to) = (Q_(enclosed))/(\varepsilon_o) --- (1)`

For r < R

`Q_(enclosed)=(\rho) ( \pi r^2 ) l`

`E*(2 \pi rl)= (\rho ( \pi r ^2 l))/(\varepsilon_o)`

`E= (\rho ( r))/(2 \varepsilon_o)`

where;

`\varepsilon_o = 8.85 * 10^(-12)`

`E= (10^(-3) ( r))/(2 (8.85 * 10^(-12)))`

`E= (10^(-3) ( r))/(2 (8.85 * 10^(-12)))`

`E = (0.56 * 10^8 ) r \ \ N/c`