An electric dipole is placed at an angle of \(30^\circ\) with an electric field intensity \(2\times10^5~ \text{N/C}\). It experiences a torque equal to \(4 ~\text{N-m}\). The charge on the dipole, if the dipole length is \(2~ \text{cm}\), is:

1.	\(8~\text{mC}\)	2.	\(2~\text{mC}\)
3.	\(5~\text{mC}\)	4.	\(7~\mu \text{C}\)

An electron falls from rest through a vertical distance \(h\) in a uniform and vertically upward-directed electric field \(E\). The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest through the same vertical distance \(h\). The fall time of the electron in comparison to the fall time of the proton is:

A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec E.\)Due to the force \(q\vec E,\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more 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. \(2~\text{m/s}, ~4~\text{m/s}\)
2. \(1~\text{m/s}, ~3~\text{m/s}\)
3. \(1~\text{m/s}, ~3.5~\text{m/s}\)
4. \(1.5~\text{m/s},~ 3~\text{m/s}\)

The electric field in a certain region is acting radially outward and is given by \(E=Ar.\) A charge contained in a sphere of radius \(a\) centered at the origin of the field will be given by:
1. \(4 \pi \varepsilon_{{o}} {A}{a}^2\)
2. \(\varepsilon_{{o}} {A} {a}^2\)
3. \(4 \pi \varepsilon_{{o}} {A} {a}^3\)
4. \(\varepsilon_{{o}} {A}{a}^3\)

What is the flux through a cube of side \(a,\) if a point charge of \(q\) is placed at one of its corners?
1. \(\frac{2q}{\varepsilon_0}\)
2. \(\frac{q}{8\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(\frac{q}{2\varepsilon_0}\)

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be:
(e is the charge on an electron)

1. $\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}$

2. $\sqrt{\frac{4\pi {\epsilon }_{0}F{d}^2}{d^2}}$

3. $\sqrt{\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}}$

4. $\frac{4\pi {\epsilon }_{0}F{d}^2}{q^2}$

A thin conducting ring of radius \(R\) is given a charge \(+Q.\) The electric field at the centre O of the ring due to 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:

                      

Three-point charges + q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:
 

A hollow cylinder has a charge q coulomb within it (at the geometrical centre). If ϕ is the electric flux in units of Volt-meter associated with the curved surface B, the flux linked with the plane surface A in units of volt-meter will be: 
    

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

2. $\frac{q}{2{\epsilon }_0}$

3. $\frac{\Phi }{3}$

4. $\frac{q}{{\epsilon }_0}-\Phi$