Question

For a cylindrical system, Prove that the electric field intensity at a point P located at a distance r from an infinite line charge with uniform charge density of ρL C/m is, E = ρ_L/(2π∈_0 r) a_r

Answer 1

If $r≥R$ , then the entire intensity vector flow will pass through the side surface of the cylinder, since the flow through both bases is zero. The cylinder side surface area formula is written as:

$2\times π\times r\times l$ . We will apply Gauss's law to a magnetic flux and we will receive:

$F=E\times 2\timesπ\times r\times l$ , and as $E=\frac{q}{4 \times π \times ε_0 \times r^2}$ , therefore $F=\frac {ρ_L\times l}{ε_0}$

said expression A is a charge of the length of the cylinder. You can then write:

$E= \frac {ρ_L} {2\times π \times ε_0 \times r}$ .