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) $2r^{2}\varepsilon _{0}E=R^{3}\rho$