If the flux of the electric field through a closed surface is zero, then consider the following statements:-

(i) the electric field must be zero everywhere on the surface.

(ii) the electric field may be zero everywhere on the surface.

(iii) the charge inside the surface must be zero.

(iv) the charge in the vicinity of the surface must be zero.

Correct statement/s are:-

1. (i), (ii)

2. (ii), (iii)

3. (ii), (iv)

4. (i), (iii)

Two point charges placed at a certain distance r in air exert a force F on each other. The distance r’ at which these charges will experience the same force in a medium of dielectric constant K is:-

$1. \frac{\mathrm{r}}{\mathrm{K}}$
$$
$2. \frac{\mathrm{r}}{\sqrt{\mathrm{K}}}$
$$
$3. \mathrm{r}\sqrt{\mathrm{K}}$
$$
$4. \mathrm{rK}$

What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

1. 0°

2. 90°

3. 180°

4. None of these

For the given figure, the direction of the electric field at A will be:

1. Along AX

2. Along AY

3. Along AZ

4. None

The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the dipole is rotated through an angle of $90°$ about its perpendicular axis, the magnitude of the electric field at the same point will be:

1. E

2. E/4

3. E/2

4. 2E

If the electric flux entering and leaving an enclosed surface respectively is ${\phi }_1 and {\phi }_2$, the electric charge inside the surface will be:

1. $({\mathrm{\phi }}_1-{\mathrm{\phi }}_2){\mathrm{\epsilon }}_0$

2. $({\mathrm{\phi }}_2-{\mathrm{\phi }}_1){\mathrm{\epsilon }}_0$

3. $({\mathrm{\phi }}_1+{\mathrm{\phi }}_2)/{\mathrm{\epsilon }}_0$

4. $({\mathrm{\phi }}_2+{\mathrm{\phi }}_1)/{\mathrm{\epsilon }}_0$

The figure shows the electric lines of force emerging from a charged body. If the electric field at A and B are ${\mathrm{E}}_{\mathrm{A}} \mathrm{and} {\mathrm{E}}_{\mathrm{B}}$ respectively and if the distance between A and B is r, then

1. $E_A>E_B$

2. $E_A<E_B$

3. $E_A=\frac{E_B}{r}$

4. $E_A=\frac{E_B}{r^2}$

In a certain region of space there is uniform electric field and gravitational field. An electron is projected with an initial velocity in a direction different from that of an electric field, then the path of the electron may be:-

(A) a straight line

(B) a circle

(C) an ellipse

(D) a parabola

1. Only (A)

2. Only (D)

3. (A) or (D)

4. (B) or (C)

In a region, an electric field E = 15 N/C making an angle $30°$ with the horizontal plane is present. A ball having charge 2 C and mass 3 kg is projected with speed 20 m/s at an angle $30°$ with the horizontal, the horizontal range of the projectile in metre is:- ($\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$)

1. 40

2. $20\sqrt{3}$

3. $40\sqrt{3}$

4. $80\sqrt{3}$

Electric field, due to an infinite line of charge, as shown in figure (a) at a point P at a distance r from the line is E. If the wire is folded at point A so that both parts lie alongside as shown in figure (b), then express electric field at P in vector form.

1. $\frac{\mathrm{E}}{2}\hat{\mathrm{i}}+\frac{\mathrm{E}}{2}\hat{\mathrm{j}}$

2. $\mathrm{E}\hat{\mathrm{i}}+\mathrm{E}\hat{\mathrm{j}}$

3. $\sqrt{2}\mathrm{E}\hat{\mathrm{i}}+\sqrt{2}\mathrm{E}\hat{\mathrm{j}}$

4. $\frac{\mathrm{E}}{\sqrt{2}}\hat{\mathrm{i}}+\frac{\mathrm{E}}{\sqrt{2}}\hat{\mathrm{j}}$