Would someone be so kind to check if I am doing this properly. I'm confused on the units, as it doesn't seem to be coming out properly.(adsbygoogle = window.adsbygoogle || []).push({});

Q) Assuming that the electric field intensity is [itex] \vec E = \hat x 100 x \,\,(V/m) [/itex], find the total electric charge contained inside a cubical volume [itex] 100 \,\, (mm) [/itex] on a side centered symmetrically at the orgin.

My Work)

Recall:

[tex] \oint \vec E \cdot d\vec s = \frac{Q}{\epsilon_0} [/tex] (Gauss's Law)

[tex] \int_V \nabla \cdot \vec A \, dv = \oint_S \vec A \cdot d\vec s [/tex] (Divergence Thm)

Thus,

[tex] \oint_S \vec E \cdot d\vec s = \int_V \nabla \cdot \vec E \, dv = \frac{Q}{\epsilon_0} [/tex]

[tex] \nabla \cdot \vec E = 100 \,\, (V/m) [/tex]

[tex] 100 (V/m) \int_V \, dv = 100\, (V/m)(100\times 10^{-3})^3(m^3) = \frac{1}{10} \,\, (V/m^2) [/tex]

[tex] \frac{1}{10} \,\, (V/m^2) = \frac{Q}{\epsilon_0} [/tex]

Thus,

[tex] Q = \frac{\epsilon_0}{10} \,\, (v/m^2) = 8.854\times 10^{-12} \frac{coul}{m^3} [/tex]

I thought the units for [itex] Q [/itex] should be in coul? Why am I getting coul per unit volume? Am I not doing this right?

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# Homework Help: Electric charge inside a cubical volume

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