Suggested languages for you:

Americas

Europe

Q68P

Expert-verifiedFound in: Page 684

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**The net electric flux through each face of a die (singular of dice) has a magnitude in units of ${{\mathbf{10}}}^{{\mathbf{3}}}{\mathbf{}}{{\mathbf{Nm}}}^{{\mathbf{2}}}{\mathbf{/}}{\mathbf{C}}$**** that is exactly equal to the number of spots N on the face (1 through 6). The flux is inward for N odd and outward for N even. What is the net charge inside the die?**

The net charge inside the die is $2.66\times {10}^{-8}\mathrm{C}$ .

- The net electric flux = ${10}^{3}\mathrm{N}.{\mathrm{m}}^{2}/\mathrm{C}$

**Gauss law describes the relation between charge and electric field in a static situation. The equation for Gauss law is,**

** ${{\mathrm{\epsilon}}}_{{0}}{\mathrm{\Phi}}{=}{{\mathrm{q}}}_{{\mathrm{enc}}}$**

**Here, ${{\mathit{q}}}_{\mathbf{e}\mathbf{n}\mathbf{c}}$is the net charge inside an imaginary closed surface and is the net flux of the electric field through the surface.**

Let ${\varnothing}_{0}={10}^{3}N.{m}^{2}/C$.

The net flux through the entire surface of the dice is given by:

$\mathit{\varnothing}\mathit{}\mathit{=}\mathit{\sum}_{\mathit{n}\mathit{-}\mathit{1}}^{\mathit{6}}{\Phi}_{\mathit{n}}\phantom{\rule{0ex}{0ex}}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{=}\mathit{\sum}_{\mathit{n}\mathit{-}\mathit{1}}^{\mathit{6}}{\left(-1\right)}^{\mathit{n}}n{\varphi}_{\mathit{0}}\phantom{\rule{0ex}{0ex}}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{=}{\varphi}_{\mathit{0}}\left(-1+2-3+4-5+6\right)\phantom{\rule{0ex}{0ex}}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{=}\mathit{3}{\varphi}_{\mathit{0}}$

Thus, the net charge enclosed is:

role="math" localid="1657360360230" $q={\epsilon}_{0}\varphi \phantom{\rule{0ex}{0ex}}=3{\epsilon}_{0}{\varphi}_{0}\phantom{\rule{0ex}{0ex}}=3\left(8.85\times {10}^{-12}{C}^{2}/N.{m}^{2}\right)\left({10}^{3}N.{m}^{2}/C\right)\phantom{\rule{0ex}{0ex}}=2.66\times {10}^{-8}C$

Therefore, the net charge inside the die is $=2.66\times {10}^{-8}C$ .

94% of StudySmarter users get better grades.

Sign up for free