The electric field components in the shown figure are ${\mathrm{E}}_{\mathrm{x}}=\alpha x^{1/2}$, E_y = E_z = 0, in which  $\mathrm{\alpha }=800<mspace\; width="1em"></mspace>\mathrm{N}/\mathrm{C}<mspace\; width="1em"></mspace>{\mathrm{m}}^{1/2}$. The net flux through the cube is: (Assume that a = 0.1 m)

$1.<mspace\; width="1em"></mspace>1.05<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$
$2.<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>2.03<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$
$3.<mspace\; width="1em"></mspace>3.05<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$
$4.<mspace\; width="1em"></mspace>4.03<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>{\mathrm{Nm}}^2{\mathrm{C}}^{-1}<mspace\; width="1em"></mspace>$

The electric field components in the shown figure are ${\mathrm{E}}_{\mathrm{x}}={\mathrm{ax}}^{1/2}$, E_y = E_z = 0, in which  $\mathrm{\alpha }=800<mspace\; width="1em"></mspace>\mathrm{N}/\mathrm{C}<mspace\; width="1em"></mspace>{\mathrm{m}}^{1/2}$. Find the charge within the cube if net flux through the cube is $1.05<mspace\; width="1em"></mspace>\mathrm{N}<mspace\; width="1em"></mspace>{\mathrm{m}}^2<mspace\; width="1em"></mspace>{\mathrm{C}}^{-1}$: (Assume that a = 0.1 m). 

$1.<mspace\; width="1em"></mspace>\mathrm{Zero}$
$2.<mspace\; width="1em"></mspace>2.7\times {10}^{-12}<mspace\; width="1em"></mspace>\mathrm{C}$
$3.<mspace\; width="1em"></mspace>7.9\times {10}^{-12}<mspace\; width="1em"></mspace>\mathrm{C}$
$4.<mspace\; width="1em"></mspace>9.2\times {10}^{-12}<mspace\; width="1em"></mspace>\mathrm{C}$

An electric field is uniform, and in the positive \(x\)-direction for positive \(x\), and uniform with the same magnitude but in the negative \(x\)-direction for negative \(x\). It is given that \(\vec{E}=200\hat{i}\) N/C for \(x>0\) and \(\vec{E}=-200\hat{i}\)  N/C for \(x<0\). A right circular cylinder of length \(20~\text{cm}\) and radius \(5~\text{cm}\) has its centre at the origin and its axis along the \(x\text{-}\)axis so that one face is at \(x= + 10~\text{cm}\) and the other is at \(x= -10~\text{cm}\) (as shown in the figure). What is the net outward flux through the cylinder?

1. \(0\)
2. \(1.57~\text{Nm}^2\text{C}^{-1}\)
3. \(3.14~\text{Nm}^2\text{C}^{-1}\)
4. \(2.47~\text{Nm}^2\text{C}^{-1}\)

An electric field is uniform, and in the positive x-direction for positive x, and uniform with the same magnitude but in the negative x-direction for negative x. It is given that E =$200<mspace\; width="1em"></mspace>\hat{i}$ N/C for x > 0 and E = –$200<mspace\; width="1em"></mspace>\hat{i}$ N/C for x < 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one face is at x = +10 cm and the other is along the x-axis so that one face is at x = +10 cm and the other is at x = –10 cm (as shown in the figure). What is the net charge inside the cylinder?

$1.<mspace\; width="1em"></mspace>2.78\times {10}^{-11}<mspace\; width="1em"></mspace>C$
$2<mspace\; width="1em"></mspace>3.10\times {10}^{-12}<mspace\; width="1em"></mspace>C$
$3.<mspace\; width="1em"></mspace>1.37\times {10}^{-10}<mspace\; width="1em"></mspace>C$
$4.<mspace\; width="1em"></mspace>2.62\times {10}^{-12}<mspace\; width="1em"></mspace>C$

An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge up to a radius R. The atom as a whole is neutral. For this model, the electric field at a distance r (r>R) from the nucleus is:

$1.<mspace\; width="1em"></mspace>\frac{Ze}{4\pi {\epsilon }_0}\left(\frac{1}{r^2}-\frac{r}{R^3}\right)$
$2.<mspace\; width="1em"></mspace>0$
$3.<mspace\; width="1em"></mspace>\frac{Ze}{4\pi {\epsilon }_0}\frac{1}{r^2}$
$4.<mspace\; width="1em"></mspace>\frac{Ze}{4\pi {\epsilon }_0}\frac{r}{R^3}$