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. $\frac{49}{500}$

The electric force on a point charge situated on the axis of a short dipole is F. If the charge is shifted along the axis to double the distance, the electric force acting will be:

1. 4F

2. $\frac{\mathrm{F}}{2}$

3. $\frac{\mathrm{F}}{4}$

4. $\frac{\mathrm{F}}{8}$

An electric dipole is placed at an angle $60°$ with an electric field of strength $4\times {10}^6$ N/C. It experiences a torque equal to $8\sqrt{3}$Nm. Calculate the charge on the dipole, if the dipole is of length 4 cm.

1. ${10}^{-1} \mathrm{C}$

2. ${10}^{-2 }\mathrm{C}$

3. ${10}^{-3} \mathrm{C}$

4. ${10}^{-4} \mathrm{C}$

A charge q is situated at the centre of a cube. The electric flux through one of the faces of the cube is:

1. $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

2. $\frac{\mathrm{q}}{3{\mathrm{\epsilon }}_0}$

3. $\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_0}$

4. Zero

A charge Q is placed at the centre of the open end of a cylindrical vessel. The electric flux through the surface of the vessel is:

1. $\frac{\mathrm{q}}{2{\mathrm{\epsilon }}_0}$

2. $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

3. $\frac{2\mathrm{q}}{{\mathrm{\epsilon }}_0}$

4. Zero

A hemispherical surface of radius R is kept in a uniform electric field E as shown in the figure. The flux through the curved surface is:

1. $2{\mathrm{E\pi R}}^2$

2. ${\mathrm{E\pi R}}^2$

3. $4{\mathrm{E\pi R}}^4$

4. Zero