Electric Charges and Fields

1. The electric field intensity near a uniformly charged infinite plane thin non-conducting sheet with charge density $+\sigma$ placed in air is

$+\frac{\sigma}{\epsilon_0}$

$+\frac{2\sigma}{\epsilon_0}$

$+\frac{3\sigma}{\epsilon_0}$

$+\frac{\sigma}{2\epsilon_0}$

2. The ratio of electric field intensity due to an electric dipole at an axial point to that at an equatorial point at the same distance from centre is

$1:1$

$1:2$

$4:1$

$2:1$

3. A charge $q$ is placed at the centre of a cube. The electric flux through one of its faces is

$\frac{q}{\epsilon_0}$

$\frac{q}{2\epsilon_0}$

$\frac{2q}{\epsilon_0}$

$\frac{q}{6\epsilon_0}$

4. The SI unit of electric dipole moment is

Newton/Coulomb

Coulomb-Newton

Joule/Coulomb

Coulomb-meter

5. The negative and positive charges of a dipole of dipole moment $\vec{p}$ are placed respectively at points $\hat{i}a$ and $+\hat{i}a$. If $y>>a$, then the electric field intensity due to the dipole at the point located at $\hat{j}y$ is

$\vec{p}\ {4 \pi \epsilon_0 y^3}$

$\vec{p}\ {2 \pi \epsilon_0 y^3}$

$-\vec{p}\ {2 \pi \epsilon_0 y^3}$

$-\vec{p}\ {4 \pi \epsilon_0 y^3}$

6. The electric field due to an electric dipole at a distance $r$ from its centre is directly proportional to

$\frac{1}{r}$

$\frac{1}{r^4}$

$\frac{1}{r^3}$

$\frac{1}{r^2}$

7. The dimension of electric flux is

$[M L^3 T^{-3} A^{-1}]$

$[M L T^{-2} A]$

$[M^{-1} L^{-1} T^{3} A]$

$[M^2 L T^{-2} A^{-1}]$

8. The value of $\frac{1}{4\pi\epsilon_0}$ in SI unit is

$9\times 10^9 N m C^{-2}$

$10^9 N m C^{-1}$

$10^9 N m^2 C^{-2}$

$9\times 10^9 N m^2 C^{-2}$

9. The law regarding lectrostatic force between two point charges is

Ampere’s law

Gauss’ law

Coulomb’s law

Faraday’s law

10. The SI unit of volume charge density is

$C m$

$C/m^3$

$C/m$

$C/m^2$

11. The magnitude of force experienced by an electron placed at a point in the electric field $\vec{E}$ is equal to its weight $m\vec{g}$. The magnitude of $\vec{E}$ is

${mg}/{e^2}$

${mg}/e$

$e^2/{(mg)}$

$mge$

12. The charge on a body is always an integral multiple of a basic quantum of charge $(e)$. This propery of electric charge is called

Conservation

Invariance

Additivity

Quantaisation

13. Due to presence of a point charge at the centre of a spherical Gaussian surface of diameter $a$, $10^6 Nm^2/C$ ammount of electric flux passes through it. Keeping the point charge at the centre, the Gaussian surface is changed to a cubical Gaussian surface of side $a$. The flux through the new Gaussian surface will be

$10^6\sqrt{2} Nm^2/C$

$2\sqrt{2}\times 10^6 Nm^2/C$

$10^6 Nm^2/C$

$\sqrt{2}\times 10^6 Nm^2/C$

14. The electric field inside a thin spherical shell of radius $R$ and uniform surface charge density $\sigma$ is

$\frac{\sigma r^2}{\epsilon_0 R^2}$

$\frac{\sigma R^2}{\epsilon_0 r^2}$

$\frac{\sigma R^2}{r^2}$

$0$

15. A proton at rest has charge $e$. When it moves with a high speed, its charge

$1/e$

$e$

$< e$

$> e$

16. The dimension of electric permitivity is

$[M^{-1} L^{-3} T^4 A^2]$

$[M^{-1} L^{-2} T^3 A^2]$

$[M L^{2} T^{-1} A^{-2}]$

$[M^2 L T^{-2} A^{-3}]$

17. The electrostatic force between two charges a distance $r$ apart in a vacuum is $F$. The force between the same charges a distance $r/2$ apart in a medium of dielectric constant $2$ is

$F/2$

$F/4$

$4F$

$2F$

18. The value of the permitivity of free space ($\epsilon_0$) in SI units is

$8.854 \times 10^{-12} C N^{-2} m^{-1}$

$8.854 \times 10^{-12} C^2 N^{-1} m^{-2}$

$9 \times 10^9 N m^2 C^{-2}$

$9 \times 10^9 N^2 m C^{-1}$

19. Force $\vec{F}$ between two charges $Q_1$ and $Q_2$ separated by $r$ is $25N$. It can be reduced to $5N$ if the separation between them is made

$\frac{r}{\sqrt{5}}$

$2r$

$\sqrt{5}r$

$\frac{r}{2}$

20. If $F_e$ and $F_g$ are the electric and gravitational forces respectively between an electron and proton situated at a distance apart, the ratio of $F_e$ and $F_g$ is of the order of

$10^{-39}$

$10^{-19}$

$10^{19}$

$10^{39}$