A very long charged solid cylinder of radius 'a' contains a uniform charge density ρ. Dielectric constant of the material of the cylinder is k. What will be the magnitude of electric field at a radial distance ' x ' (x

Question

A very long charged solid cylinder of radius 'a' contains a uniform charge density ρ. Dielectric constant of the material of the cylinder is k. What will be the magnitude of electric field at a radial distance ' x ' (x< a) from the axis of the cylinder? (A) ρ (x/ε0) (B) ρ (x/2 k ε0) (C) ρ (x2/2 a ε0) (D) ρ (x2/2 k)

Tardigrade Admin · Accepted Answer

Using Gauss's Law E(2 π x l)=(ρ(π x2 l)/k ε0) ∴ E=(ρ x/2 k ε0)

Q. A very long charged solid cylinder of radius ' $a$ ' contains a uniform charge density $ρ$ . Dielectric constant of the material of the cylinder is $k$ . What will be the magnitude of electric field at a radial distance ' $x$ ' $(x < a)$ from the axis of the cylinder?

$ρ \frac{x}{ε _{0}}$

$ρ \frac{x}{2 k ε _{0}}$

$ρ \frac{x ^{2}}{2 a ε _{0}}$

$ρ \frac{x ^{2}}{2 k}$

Using Gauss's Law
$E (2 π x l) = \frac{ρ ( π x ^{2} l )}{k ε _{0}}$
$∴ E = \frac{ρ x}{2 k ε _{0}}$

Q. A very long charged solid cylinder of radius 'a' contains a uniform charge density ρ. Dielectric constant of the material of the cylinder is k. What will be the magnitude of electric field at a radial distance ' x ' (x<a) from the axis of the cylinder?

ρε0​x​

ρ2kε0​x​

ρ2aε0​x2​

ρ2kx2​