A sphere of radius r has an electric charge uniformly distributed in its entire volume. At a distance d from the centre inside the sphere (d<r) the electric field intensity is directly proportional to:

1. $\frac{1}{\mathrm{d}}$

2. $\frac{1}{{\mathrm{d}}^2}$

3. d

4. ${\mathrm{d}}^2$

The electric field at a distance 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance $\frac{\mathrm{R}}{2}$ from the centre will be:

1. Zero

2. 2E

3. 4E

4. 16E

In a uniform electric field if a charge is fired in a direction different from the line of the electric field, then the trajectory of the charge will be a:

1. straight line

2. circle

3. parabola

4. ellipse

A positively charged pendulum is oscillating in a uniform electric field pointing upwards. Its time period as compared to that when it oscillates without electric field:

1. is less.

2. is more.

3. remains unchanged.

4. starts fluctuating.

How many electrons should be removed from a coin of mass 1.6 g so that it may float in an electric field of intensity ${10}^9$ N/C directed upwards?

1. $9.8\times {10}^7$

2. $9.8\times {10}^5$

3. $9.8\times {10}^3$

4. $9.8\times {10}^1$

ABC is an equilateral triangle. Charges +q are placed at each corner. The electric field intensity at the centroid of the triangle will be:

1. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\times \frac{\mathrm{q}}{{\mathrm{r}}^2}$

2. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\times \frac{3\mathrm{q}}{{\mathrm{r}}^2}$

3. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\times \frac{\mathrm{q}}{\mathrm{r}}$

4. Zero

A charge Q is placed at the centre of a square. If the electric field intensity due to the charges at the corners of the square is E₁ and the intensity at the midpoint of the side of the square is E₂, then the ratio $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}$ will be:

1. $\frac{1}{2\sqrt{2}}$

2. $\sqrt{2}$

3. $\frac{1}{2}$

4. $2$

Point charges, each of magnitude Q, are placed at the three corners of a square as shown in the diagram. What is the direction of the resultant electric field at point A?

1. OC

2. OE

3. OD

4. OB

Two charges e and 3e are placed at a distance r. The distance of the point where the electric field intensity will be zero is:

1. $\frac{\mathrm{r}}{(1+\sqrt{3})}$ from 3e charge.

2. $\frac{\mathrm{r}}{(1+\sqrt{3})}$ from e charge.

3. $\frac{\mathrm{r}}{(1-\sqrt{3})}$ from 3e charge.

4. $\frac{\mathrm{r}}{1+\sqrt{{\displaystyle \frac{1}{3}}}}$ from e charge.

If the electric lines of force in a region are represented as shown in the figure, then one can conclude that the electric field is:

1. Non-uniform

2. Uniform

3. Both uniform and non-uniform

4. Zero everywhere