Question

A long solid non-conducting cylinder of radius $10\text{cm}$ contains a uniformly distributed charge of density $10{\text{nC/m}}^3$. Find the magnitude of electric field at a point $\text{P}$ inside the cylindrical volume at a distance $5\text{cm}$ from its axis.
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

• A. $17.8\text{N/C}$
• B. $27.8\text{N/C}$
• C. $37.8\text{N/C}$
• D. $47.8\text{N/C}$

Answer 1

The correct option is B $27.8\text{N/C}$

We know that, electric field at a point inside a non-conducting solid cylinder is given by

$E=\frac{\rho r}{2{ϵ}_0}$

Here,

$\sigma =10{\text{nC/m}}^3=10\times {10}^{-9}{\text{C/m}}^3$

$r=5\text{cm}=5\times {10}^{-2}\text{m}$

$E=\frac{10\times {10}^{-9}\times 5\times {10}^{-2}}{2\times 9\times {10}^{-12}}$

$E=27.8\text{N/C}$