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. \(\dfrac{Z e}{4 \pi \varepsilon_{0}} \left(\dfrac{1}{r^{2}} - \dfrac{r}{R^{3}}\right)\)
2. \( \dfrac{Z e}{4 \pi \varepsilon_{0}} \dfrac{1}{R^{2}}\)
3. \( \dfrac{Z e}{4 \pi \varepsilon_{0}} \dfrac{1}{r^{2}}\)
4. \(  \dfrac{Z e}{4 \pi \varepsilon_{0}} \dfrac{r}{R^{3}}\)

The accelerations of electron and proton due to the electrical force of their mutual attraction when they are 1 Å (=${10}^{-10} m$) apart are respectively: (\(m_p=1.67\times10^{-27}~\text{kg},~m_e=9.11\times10^{-31}~\text{kg}\))

Two point charges +8q and -2q are located at x=0 and x=L respectively. The point on x axis at which net electric field is zero due to these charges is-
1.  8L
2.  4L
3.  2 L
4.  L

Two point charges placed in a medium of dielectric constant 5 are at a distance r between them, experience an electrostatic force ‘F’. The electrostatic force between them in vacuum at the same distance r will be-
1.  5F
2.  F
3.  F/2
4.  F/5

Which statement is true for Gauss law-
1.  All the charges whether inside or outside the gaussian surface contribute to the electric flux.
2.  Electric flux depends upon the geometry of the gaussian surface.
3.  Gauss theorem can be applied to non-uniform electric field.
4.  The electric field over the gaussian surface remains continuous and uniform at every point.

A cylinder of radius r and length l is placed in an uniform electric field parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by-
1.  zero
2.  ${\mathrm{\pi r}}^2$
3.  E${\mathrm{\pi r}}^2$
4. 2E${\mathrm{\pi r}}^2$

Polar molecules are the molecules:

A dipole is placed in an electric field as shown. In which direction will it move? 

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 =$200 \hat{i}$ N/C for x > 0 and E = –$200 \hat{i}$ 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?

$1. 2.78\times {10}^{-11} C$
$2 3.10\times {10}^{-12} C$
$3. 1.37\times {10}^{-10} C$
$4. 2.62\times {10}^{-12} C$

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. \(2.47~\text{Nm}^2\text{C}^{-1}\)