A spherical volume has a uniformly distributed charge of density 2.0 10⁻⁴ C m ⁻³ . Determine the electric field at a point located inside the volume, at a distance of 4.0 cm from the centre.

Step-by-step solution

By Gauss's law, the electric field inside a uniformly charged solid sphere at a distance r from the centre is given by: E d A = q_ enclosed ₀ E (4 r^2) = 4 3 r^3 ₀ E = r 3 ₀ Substituting the given values, = 2.0 10⁻⁴ C m ⁻³ , r = 4.0 10⁻² m and ₀ = 8.85 10⁻¹² C ^2 N ⁻¹ m ⁻² : E = 2.0 10⁻⁴ 4.0 10⁻² 3 8.85 10⁻¹² E = 8.0 10⁻⁶ 26.55 10⁻¹² E 3.01 10^5 N C ⁻¹