Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

1. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2 }{e^2}$                  2. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fe}}^2}{d^2}}$

3. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{e^2}}$               4. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{q^2}$

 

Two particles of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any force. The value of $\frac{q}{m}$ is 

(1) l

(2) $\sqrt{\frac{\pi {\epsilon }_0}{G}}$

(3) $\sqrt{\frac{G}{4\pi {\epsilon }_0}}$

(4) $\sqrt{4\pi {\epsilon }_{0}G}$

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

You are traveling in a car during a thunderstorm. In order to protect yourself from lightning, you would prefer to

(1) Touch the nearest electric pole

(2) Take shelter under a tree

(3) Get out and crouch on the ground

(4) Remain in the car

Two-point charges \(+8q\) and \(-2q\) are located at \(x=0\) and \(x=L\) respectively. The location of a point on the \(x\text-\)axis at which the net electric field due to these two point charges is zero is:
1. \(8L\)
2. \(4L\)
3. \(2L\)
4. \(\frac{L}{4}\)

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

Eight dipoles of charges of magnitude e are placed inside a cube. The total electric flux coming out of the cube will be 

(1) $\frac{8e}{{\epsilon }_0}$

(2) $\frac{16e}{{\epsilon }_0}$

(3) $\frac{e}{{\epsilon }_0}$

(4) Zero 

The electrostatic field due to a charged conductor just outside the conductor is 

1. zero and parallel to the surface at every point inside the conductor

2. zero and is normal to the surface at every point inside the conductor

3. parallel to the surface at every point and zero inside the conductor

4. normal to the surface at every point and zero inside the conductor

The dimension of (1/2) ${\epsilon }_0{E}^2 ({\epsilon }_0$: permittivity of free space; E: electric field) is

(1) MLT^–1

(2) ML²L^–2

(3) ML^–1T^–2

(4) ML²T^–1

\(q_1, q_2, q_3~\text{and}~q_4\) are point charges located at points as shown in the figure and \(S\) is a spherical Gaussian surface of radius \(R\). Which of the following is true according to the Gauss’s law?