An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like 

(1) A

(2) B

(3) C

(4) D

The figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?

(1) 1

(2) 2

(3) 3

(4) 4

An electric charge q is placed at the centre of a cube of side a. The electric flux on one of its faces will be:

(1) $\frac{q}{6{\epsilon }_0}$

(2) $\frac{q}{{\epsilon }_0{a}^2}$

(3) $\frac{q}{4\pi {\epsilon }_0{a}^2}$

(4) $\frac{q}{{\epsilon }_0}$ 

Total electric flux coming out of a unit positive charge put in air is 

(1) ${\epsilon }_0$

(2) ${\epsilon }_0^{-1}$

(3) ${\left(4p{\epsilon }_0\right)}^{-1}$

(4) $4\pi {\epsilon }_0$ 

A cube of side l is placed in a uniform field E, where $E=E\hat{i}$. The net electric flux through the cube is

(1) Zero

(2) l²E

(3) 4l²E

(4) 6l²E

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is 

(1) $3q/{\epsilon }_0$

(2) $2q/{\epsilon }_0$

(3) $q/{\epsilon }_0$ 

(4) Zero

Consider the charge configuration and spherical Gaussian surface as shown in the figure. While calculating the flux of the electric field over the spherical surface, the electric field will be due to: 

(1) q₂ only

(2) Only the positive charges

(3) All the charges

(4) +q₁ and – q₁ only

Two-point charges \(+q\) and \(–q\) are held fixed at \((–d, 0)\) and \((d, 0)\) respectively of a \((x, y)\) coordinate system. Then:

The electric field due to a uniformly charged solid sphere of radius R as a function of the distance from its centre is represented graphically by -

(1)  (2)

(3)  (4)

Suppose the charge of a proton and an electron differ slightly. One of them is \(\text- e\) and the other is \((e+\Delta e)\). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then $$\(\Delta e\) is of the order: [Given the mass of hydrogen, ${}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)]
1. \(10^{-20}~\text{C}\)
2. \(10^{-23}~\text{C}\)
3. \(10^{-37}~\text{C}\)
4. \(10^{-47}~\text{C}\)