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

An uncharged sphere of metal is placed in a uniform electric field produced by two oppositely charged plates. The lines of force will appear as:

1. 

2. 

3. 

4. 

An electron released on the axis of a positively charged ring at a large distance from the centre will:

1. not move.

2. do oscillatory motion.

3. do SHM.

4. do non-periodic motion.

The figure shows electric lines of forces due to charges Q₁ and Q₂. Hence,

1. Q₁ and Q₂ both are negative.

2. Q₁ and Q₂ both are positive.

3. Q₁ > Q₂ 

4. Both (2) and (3)

The figure shows the electric lines of force. If E_x and E_y are the magnitudes of the electric field at points x and y respectively, then:

1. ${\mathrm{E}}_{\mathrm{x}}>{\mathrm{E}}_{\mathrm{y}}$

2. ${\mathrm{E}}_{\mathrm{x}}={\mathrm{E}}_{\mathrm{y}}$

3. ${\mathrm{E}}_{\mathrm{x}}<{\mathrm{E}}_{\mathrm{y}}$

4. Any of these

Electric charges Q, Q and -2Q respectively are placed at the three corners of an equilateral triangle of side a. The magnitude of the electric dipole moment of the system is:

1. $\sqrt{2}\mathrm{Qa}$

2. $\sqrt{3}\mathrm{Qa}$

3. Qa

4. 2Qa

An electric dipole placed in a uniform electric field experiences a maximum moment of couple when the dipole is placed:

1. against the direction of the field.

2. towards the electric field.

3. perpendicular to the direction of the field.

4. at $135°$ to the direction of the field.

The force of interaction between two co-axial short electric dipoles whose centres are R distance apart varies as:

1. $\frac{1}{\mathrm{R}}$

2. $\frac{1}{{\mathrm{R}}^2}$

3. $\frac{1}{{\mathrm{R}}^3}$

4. $\frac{1}{{\mathrm{R}}^4}$

Two charges of $+25\times {10}^{-9}$ coulomb and $-25\times {10}^{-9}$ coulomb are placed 6m apart. Find the electric field intensity ratio at points 4 m from the centre of the electric dipole (i) on the axial line (ii) on the equatorial line

1. $\frac{1000}{49}$

2. $\frac{49}{1000}$

3. $\frac{500}{49}$

4. $\frac{49}{500}$