# QB/c19ElectricPotentialField GaussLaw

< QB

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% See special:permalink/1863398 for a wikitext version of this quiz.

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\title{c19ElectricPotentialField\_GaussLaw}
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Attribution for each question is documented in the Appendix}
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\question A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$.  The height is much less than the radius: $$H << R$$. The electric field at the center vanishes.  What formula describes the electric field at a distance, z, on axis from the center if $$z>H/2$$?\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863398}}}\fi
\begin{choices}
\choice answer:  $$\varepsilon_0 E= \rho z$$
\choice answer:  $$\varepsilon_0 E= H\rho$$
\choice answer:  $$\varepsilon_0 E= H\rho z$$
\CorrectChoice answer:  $$\varepsilon_0 E = H\rho /2$$
\choice answer:  $$\varepsilon_0 E = r\rho$$
\end{choices}

\question A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$.  The height is much less than the radius: $$H << R$$. The electric field at the center vanishes.  What formula describes the electric field at a distance, z, on axis from the center if $$z<H/2$$?\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863398}}}\fi
\begin{choices}
\choice answer:  $$\varepsilon_0 E = H\rho /2$$
\choice answer:  $$\varepsilon_0 E= \rho z/2$$
\CorrectChoice answer:  $$\varepsilon_0 E= \rho z$$
\choice answer:  $$\varepsilon_0 E= H\rho$$
\choice answer:  $$\varepsilon_0 E= H\rho z$$
\end{choices}

\question A sphere has a uniform charge density of $$\rho$$, and a radius or R.  What formula describes the electric field at a distance $$r>R$$?\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863398}}}\fi
\begin{choices}
\choice answer:  $$r^2\varepsilon_0 E=rR^2\rho /2$$
\choice answer:  $$r^2\varepsilon_0 E=R^3\rho /2$$
\choice answer:  $$r^2\varepsilon_0 E= r^3\rho/3$$
\choice answer:  $$r^2\varepsilon_0 E=r^3\rho /2$$
\CorrectChoice answer:  $$r^2\varepsilon_0 E=R^3\rho /3$$
\end{choices}

\question A sphere has a uniform charge density of $$\rho$$, and a radius equal to R.  What formula describes the electric field at a distance $$r<R$$?\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863398}}}\fi
\begin{choices}
\choice answer:  $$r^2\varepsilon_0 E=r^3\rho /2$$
\choice answer:  $$r^2\varepsilon_0 E=R^3\rho /3$$
\choice answer:  $$r^2\varepsilon_0 E=Rr^2\rho /3$$
\CorrectChoice answer:  $$r^2\varepsilon_0 E=r^3\rho /3$$
\choice answer:  $$r^2\varepsilon_0 E=R^3\rho /2$$
\end{choices}

\question A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$.  The height is much greater than the radius: $$H >> R$$?. The electric field at the center vanishes.  What formula describes the electric field at a distance, r, radially from the center if $$r<R$$? \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863398}}}\fi
\begin{choices}
\choice answer:  $$2R\varepsilon_0 E= r^2\rho$$
\choice answer:  $$2r\varepsilon_0 E = R^2\rho$$
\CorrectChoice answer:  $$2\varepsilon_0 E = r\rho$$
\choice answer:  $$2\varepsilon_0 E = R\rho$$
\choice answer:  $$2r^2\varepsilon_0 E= R^3 \rho$$
\end{choices}

\question A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$.  The height is much greater than the radius: $$H >>$$. The electric field at the center vanishes.  What formula describes the electric field at a distance, r, radially from the center if $$r>R$$?\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863398}}}\fi
\begin{choices}
\choice answer:  $$2R\varepsilon_0 E= r^2\rho$$
\choice answer:  $$2\varepsilon_0 E = r\rho$$
\CorrectChoice answer:  $$2r\varepsilon_0 E = R^2\rho$$
\choice answer:  $$2r\varepsilon_0 E = 2R^2\rho$$
\choice answer:  $$2r^2\varepsilon_0 E= R^3 \rho$$
\end{choices}

\end{questions}
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