Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is \(r\) (as shown in Fig. I). Now, as shown in Fig. II, the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:
     
1. \(\frac{r}{\sqrt[3]{2}}\)
2. \(\frac{r}{\sqrt[2]{2}}\)
3. \(\frac{2r}{3}\)
4. none of the above

A thin conducting ring of the 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 \(\phi\) 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. \(\frac{1}{2}\left(\frac{q}{\varepsilon_0}-\phi\right)\)
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{\phi}{3}\)
4. \(\frac{q}{\varepsilon_0}-\phi\)

A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:

Two parallel infinite line charges with linear charge densities \(+\lambda~\text{C/m}\) and \(+\lambda~\text{C/m}\) are placed at a distance \({R}.\) The electric field mid-way between the two line charges is: