Physics

Physics

Problem

30. A solid nonconducting sphere of radius R has a charge Q uniformly distributed throughout its volume. A Gaussian surface of radius r with r<R\mathrm{r}<\mathrm{R} is used to calculate the magnitude of the electric field E at a distance r from the center of the sphere. Which of the following equations results from a correct application of Gauss's law for this situation? A) E(4πR2)=Q/ε0E\left(4 \pi R^{2}\right)=Q / \varepsilon_{0} B) E(4πr2)=Q/ε0E\left(4 \pi r^{2}\right)=Q / \varepsilon_{0} C) E(4πr2)=(Q3r3)/(ε04πR)\mathrm{E}\left(4 \pi \mathrm{r}^{2}\right)=\left(\mathrm{Q} 3 \mathrm{r}^{3}\right)/\left(\varepsilon_{0} 4 \pi \mathrm{R}\right) D) E(4πr2)=(Qr3)/(ε0R3)\mathrm{E}\left(4 \pi \mathrm{r}^{2}\right)=\left(\mathrm{Qr}^{3}\right)/\left(\varepsilon_{0} \mathrm{R}^{3}\right) E) E(4πr2)=0\mathrm{E}\left(4 \pi \mathrm{r}^{2}\right)=0 A) E(4πR2)=Q/ε0E\left(4 \pi R^{2}\right)=Q / \varepsilon_{0} B) E(4πr2)=Q/ε0E\left(4 \pi r^{2}\right)=Q / \varepsilon_{0} C) E(4πr2)=(Q3r3)/(ε04πR)\mathrm{E}\left(4 \pi \mathrm{r}^{2}\right)=\left(\mathrm{Q} 3 \mathrm{r}^{3}\right)/\left(\varepsilon_{0} 4 \pi \mathrm{R}\right) D) E(4πr2)=(Qr3)/(ε0R3)\mathrm{E}\left(4 \pi \mathrm{r}^{2}\right)=\left(\mathrm{Qr}^{3}\right)/\left(\varepsilon_{0} \mathrm{R}^{3}\right) E) E(4πr2)=0\mathrm{E}\left(4 \pi \mathrm{r}^{2}\right)=0

Browse the problem library