A hollow cylinder has a charge q coulomb within it. If $\varnothing$ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of voltmeter will be

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

2. $\frac{\varnothing }{3}$

3. $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}-\varnothing$

4. $\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-\varnothing \right)$

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

1. 3 E along OK

2. 3 E along KO

3. E along OK

4. E along KO

A square surface of side L meter in the plane of the paper is placed in a uniform electric field E $\left({\mathrm{Vm}}^{-1}\right)$ acting along the same plane at an angle $\mathrm{\theta }$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface, in units of Vm, is

1. zero

2. ${\mathrm{EL}}^2$

3. ${\mathrm{EL}}^2\mathrm{cos\theta }$

4. ${\mathrm{EL}}^2\mathrm{sin\theta }$

Two parallel metal plates having charges +Q and -Q face each other at a certain distance them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

1. increase

2. decrease

3. remain same

4. become zero

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. E

2. $\frac{E}{2}$

3. $\frac{E}{3}$

4. zero

What is the flux through a cube of side 'a' if a point charge of q is at one of the corners?

1. $\frac{2q}{{\epsilon }_0}$

2. $\frac{q}{8{\epsilon }_0}$

3. $\frac{q}{{\epsilon }_0}$

4. $\frac{q}{2{\epsilon }_0}6a^2$

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\mathrm{\theta }$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\mathrm{\theta }=90°$, the torque and the potential energy of the dipole will, respectively, be

1. $\mathrm{pE} \mathrm{sin\theta }, 2\mathrm{pE} \mathrm{cos\theta }$

2. $\mathrm{pE} \mathrm{sin\theta }, -\mathrm{pE} \mathrm{sin\theta }$

3. $\mathrm{pE} \mathrm{sin\theta }, -\mathrm{pE} \mathrm{cos\theta }$

4. $\mathrm{pE} \mathrm{sin\theta }, -2\mathrm{pE} \mathrm{cos\theta }$

An electric dipole is placed at an angle of $30°$ with electric field intensity $2\times {10}^5 N C^{-1}$. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

1. 2 mC

2. 5 mC

3. $7\mathrm{\mu C}$

4. 8 mC

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{\mathrm{E}}$. Due to the force $\mathrm{q}\overrightarrow{\mathrm{E}}$, its velocity increases from 0 to 6 m ${\mathrm{s}}^{-1}$ in one second duration. At that instant the direction of the field is reversed. The car continues to move for two seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively.

1. $1 m s^{-1}, 3.5 m s^{-1}$

2. $1 m s^{-1}, 3 m s^{-1}$

3. $2 m s^{-1}, 4 m s^{-1}$

4. $1.5 m s^{-1}, 3 m s^{-1}$

An electric dipole has the magnitude of its charge as q and its dipole moment is $\overrightarrow{\mathrm{p}}$. It is placed i a uniform electric field $\overrightarrow{\mathrm{E}}$. If its dipole moment is along the direction of the field the force on it and its potential energy are, respectively

1. $\mathrm{q}.\overrightarrow{\mathrm{E}} \mathrm{and} \overrightarrow{\mathrm{p}}.\overrightarrow{\mathrm{E}}$

2. zero and minimum

3. $\mathrm{q}.\overrightarrow{\mathrm{E}} \mathrm{and} \mathrm{maximum}$

4. $\mathrm{q}.\overrightarrow{\mathrm{E}} \mathrm{and} \mathrm{minimum}$