The dielectric constant of pure water is 81. Its permittivity will be:

1. 7.12 × 10^–10 MKS units

2. 8.86 × 10^–12 MKS units

3. 1.02 × 10¹³ MKS units

4. Cannot be calculated

Force of attraction between two point charges Q and – Q separated by d meter is F_e. When these charges are given to two identical spheres of radius R = 0.3 d whose centres are d meter apart, the force of attraction between them is 

1. Greater than F_e

2. Equal to F_e

3. Less than F_e

4. None of the above

One metallic sphere A is given a positive charge whereas another identical metallic sphere B of the exact same mass as of A is given an equal amount of negative charge. Then:

(1) mass of A and mass of B are the same.

(2) mass of A is more.

(3) mass of B is less.

(4) mass of B is more.

Two charges each equal to 2μC are 0.5m apart. If both of them exist inside the vacuum, then the force between them is 

(1) 1.89 N

(2) 2.44 N

(3) 0.144 N

(4) 3.144 N

A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge –Q. The surface charge density on the inner and outer surfaces of the spherical shell will be?

(1) $-\frac{2\mathrm{Q}}{4{\mathrm{\pi b}}^2}, \frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(2) $-\frac{\mathrm{Q}}{4{\mathrm{\pi b}}^2}, \frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(3) $0, \frac{\mathrm{Q}}{4{\mathrm{\pi c}}^2}$

(4) None of the above

Three charges are placed at the vertices of an equilateral triangle of side ‘a’ as shown in the following figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is 

(1) $Q^2/\left(4\pi {\epsilon }_0{a}^2\right)$

(2) $-Q^2/\left(4\pi {\epsilon }_0{a}^2\right)$

(3) Zero

(4) $Q^2/\left(2\pi {\epsilon }_0{a}^2\right)$

Two particles of equal mass \(m\) and charge \(q\) are placed at a distance of \(16~\text{cm}\). They do not experience any net force. The value of \(\frac{q}{m}\) is: 
1. \(l\)
2. \(\sqrt{\frac{\pi \varepsilon_0}{G}}\)
3. \(\sqrt{\frac{G}{4\pi \varepsilon_0}}\)
4. \(\sqrt{4\pi \varepsilon_0 G}\)

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force $\overrightarrow{F}$ on electron is (Where $K=\frac{1}{4\pi {\epsilon }_0}$) 

(1) $-K\frac{e^2}{r^3}\hat{r}$

(2) $K\frac{e^2}{r^3}\overrightarrow{r}$

(3) $-K\frac{e^2}{r^3}\overrightarrow{r}$

(4) $K\frac{e^2}{r^2}\hat{r}$