Question

For the given graph between electric field $\left(E\right)$ at a point and distance $\left(x\right)$ of this point from the mid-line of an infinitely long uniformly charged non-conducting thick sheet, the volume charge density of the given sheet is:-
[$d$ is the thickness of the sheet]

• A. $3\times {10}^{-12}{\text{C/m}}^3$
• B. $9\times {10}^{-12}{\text{C/m}}^3$
• C. $12\times {10}^{-12}{\text{C/m}}^3$
• D. $15\times {10}^{-12}{\text{C/m}}^3$

Answer 1

The correct option is B $9\times {10}^{-12}{\text{C/m}}^3$


Electric field for a point inside the thick sheet is given by

$E=\frac{\rho x}{{ϵ}_0}$

$\Rightarrow \frac{E}{x}=\frac{\rho }{{ϵ}_0}$

$\Rightarrow \tan {45}^{\circ }=\frac{\rho }{{ϵ}_0}=1\text{N/Cm}$ [from graph]

$\Rightarrow \rho ={ϵ}_0=9\times {10}^{-12}{\text{C/m}}^3$

So, option $\left(b\right)$ is correct.