Question

Based on the given graph between electric field $\left(E\right)$ and distance $\left(r\right)$ from axis of the infinite uniformly charged solid non-conducting cylinder, the charge density is
[$R$ is radius of cylinder]

• A. $2.8\times {10}^{-11}{\text{C/m}}^3$
• B. $0.8\times {10}^{-11}{\text{C/m}}^3$
• C. $3.8\times {10}^{-11}{\text{C/m}}^3$
• D. $1.8\times {10}^{-11}{\text{C/m}}^3$

Answer 1

The correct option is D $1.8\times {10}^{-11}{\text{C/m}}^3$

We know that the electric field ($E$) at a distance $\left(r\right)$ from the axis of an infinite uniformly charged solid non-conducting cylinder inside it is given by
$E=\frac{\rho r}{2{ϵ}_0}$ where $\rho$ is charge density
$\Rightarrow \frac{E}{r}=\frac{\rho }{2{ϵ}_0}$
$\Rightarrow \tan {45}^{\circ }=\frac{\rho }{2{ϵ}_0}$ [from graph]
$\Rightarrow \rho =2{ϵ}_0$
$\Rightarrow \rho =2\times 9\times {10}^{-12}$
$\Rightarrow \rho =1.8\times {10}^{-11}{\text{C/m}}^3$