Physics equations/19-Electric Potential and Electric Field/Q:UsingGaussLaw

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A
{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?} - $$\varepsilon_0 E=   \rho z $$ -b) $$\varepsilon_0 E=  H\rho $$ -c) $$\varepsilon_0 E=   H\rho z$$ -d) none of these are correct +e) $$\varepsilon_0 E = H\rho /2$$ {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?} - $$\varepsilon_0 E = H\rho /2$$ -b) none of these are correct +c) $$\varepsilon_0 E=   \rho z $$ -d) $$\varepsilon_0 E=  H\rho $$ -e) $$\varepsilon_0 E=   H\rho z$$ {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?} - none of these are correct -b) $$ r^2\varepsilon_0 E=R^3\rho /2$$ -c) $$ r^2\varepsilon_0 E= r^3\rho/3$$ -d) $$ r^2\varepsilon_0 E=r^3\rho /2$$ +e) $$ r^2\varepsilon_0 E=R^3\rho /3$$ {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?} - $$ r^2\varepsilon_0 E=r^3\rho /2$$ -b) $$ r^2\varepsilon_0 E=R^3\rho /3$$ -c) none of these are correct +d) $$ r^2\varepsilon_0 E=r^3\rho /3$$ -e) $$ r^2\varepsilon_0 E=R^3\rho /2$$ {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? } - $$2R\varepsilon_0 E=  r^2\rho $$ -b) $$2r\varepsilon_0 E = R^2\rho $$ +c) $$2\varepsilon_0 E =  r\rho $$ -d) none of these are correct -e) $$2r^2\varepsilon_0 E= R^3  \rho $$ {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?} - $$2R\varepsilon_0 E=  r^2\rho $$ -b) $$2\varepsilon_0 E = r\rho $$ +c) $$2r\varepsilon_0 E =  R^2\rho $$ -d) none of these are correct -e) $$2r^2\varepsilon_0 E= R^3  \rho $$