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.

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Quantrex Academy · Accepted Answer

Correct answer: D. 3.0 × 10^5 N C^ -1

By Gauss's law, the electric field inside a uniformly charged solid sphere at a distance

r

from the centre is given by:

\oint \vec{E} \cdot d\vec{A} = \dfrac{q_{\text{enclosed}}}{\varepsilon_0}

E (4 \pi r^2) = \dfrac{\dfrac{4}{3} \pi r^3 \rho}{\varepsilon_0}

E = \dfrac{\rho r}{3 \varepsilon_0}

Substituting the given values,

\rho = 2.0 \times 10^{-4} \text{ C m}^{-3}

,

r = 4.0 \times 10^{-2} \text{ m}

and

\varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}

:

E = \dfrac{2.0 \times 10^{-4} \times 4.0 \times 10^{-2}}{3 \times 8.85 \times 10^{-12}}

E = \dfrac{8.0 \times 10^{-6}}{26.55 \times 10^{-12}}

E \approx 3.01 \times 10^5 \text{ N C}^{-1}

A spherical volume has a uniformly distributed charge of density...

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