Question

A spherical volume contains a uniformly distributed charge of density $2.0\times {10}^{-4}C/m^3$. Find the electric field at a point inside the volume at a distance $4.0cm$ from the center.

Answer 1

Given : Volume charge density $=2.0\times {10}^{-4}c/m^3$

In order to find the electric field at a point $4cm=4\times {10}^{-2}m$ from the centre let us assume a concentric.

spherical surface inside the sphere.

Now, $\oint Eds=\frac{q}{{\in }_0}$

But the charge density is given as:

$\sigma =\frac{q}{4/3\pi R^3}$

so, $q=\sigma \times 4/3\pi R^3$

Hence The electric field can be obtained as:

$E=\frac{\sigma \times 4/3\times 22/7\times (4\times {10}^{-2}{)}^3}{{\in }_0}\times \frac{1}{4\times 22/7\times (4\times {10}^{-2}{)}^2}$

$E=2.0\times {10}^{-4}1/3\times 4\times {10}^{-2}\times 18.85\times {10}^{-12}=3.0\times {10}^{5}N/C$