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

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A

1. 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

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

3. 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

4. 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

5. 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

6. 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

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