A gold-leaf electroscope is given a positive charge, causing its foil leaves to separate. When an object is brought near the top plate of the electroscope, the foils separate even further. We could conclude:

1.  that the object is positively charged.

2.  that the object is electrically neutral.

3.  that the object is negatively charged.

4.  none of these.

The electric field at a distance $\frac{3\mathrm{R}}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{\mathrm{R}}{2}$ from the centre of the sphere is:-

1. zero

2. E

3. $\frac{\mathrm{E}}{2}$

4. $\frac{\mathrm{E}}{3}$

Two positive point charges, each of magnitude 10 C are fixed at positions A & B at a separation 2d = 6m. A negatively charged particle of mass m = 90 gm and charge of magnitude -$10 \mathrm{x} {10}^{-6} \mathrm{C}$ is revolving in a circular path of radius 4 m in the plane perpendicular to the line AB and bisecting the line AB. Neglect the effect of gravity. Find the angular velocity of the particle:-

1. 200 rad/s

2. 400 rad/s

3. 250 rad/s

4. 100 rad/s

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

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. $80\sqrt{3}$

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)

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