Question

A spherical volume has a uniformly distributed charge density $2\times {10}^{-4}C{m}^{-3}$. The electric field at a point inside the volume at a distance 4.0 cm from the centre is :

• A. $3.01\times {10}^{5}N{C}^{-1}$
• B. $2.1\times {10}^{5}N{C}^{-1}$
• C. $6.2\times {10}^{5}N{C}^{-1}$
• D. none of these

Answer 1

Answer: (A)

$3.01\times {10}^{5}N{C}^{-1}$

Using Gauss's law the electric field inside the sphere , $E.4\pi r^2=\frac{Q_{en}}{{ϵ}_0}=\frac{\rho .\left(4/3\right)\pi r^3}{{ϵ}_0}$

$\Rightarrow E=\frac{\rho r}{3{ϵ}_0}=\frac{2\times {10}^{-4}\times 4\times {10}^{-2}}{3\times 8.854\times {10}^{-12}}=3.01\times {10}^{5}N{C}^{-1}$