A hollow conducting sphere is placed in an electric field produced by a point charge placed at \(P\) as shown in the figure. Let\(​​V_A ~,V_B~,V_C\) be the potentials at points \(A\), \(B\) and \(C\) respectively. Then:

        
1. \(V_A<V_B<V_C\)
2. \(V_A>V_B>V_C\)
3. \(V_C>V_B=V_A\)
4. \(V_A=V_B=V_C\)

Four particles each having charge q are placed at the vertices of a square of side a. The value of the electric potential at the midpoint of one of the side will be

1.  0

2.  $\frac{1}{4\pi {ϵ}_0}\frac{2q}{a}(2+\frac{2}{\sqrt{5}})$

3.  $\frac{1}{4\pi {ϵ}_0}\frac{2q}{a}(2-\frac{2}{\sqrt{5}})$

4.  $\frac{1}{4\pi {ϵ}_0}\frac{2q}{a}(1+\frac{1}{\sqrt{5}})$

The electric potential at a point at distance 'r' from a short dipole is proportional to

1. $r^2$

2. ${\mathrm{r}}^{-1}$

3. $r^{-2}$

4. $r^1$

A hollow charged metal spherical shell has radius R. If the potential difference between its surface and a point at a distance 3R from the center is V, then the value of electric field intensity at a point at distance 4R from the center is

1.  $\frac{3\mathrm{V}}{19\mathrm{R}}$

2.  $\frac{\mathrm{V}}{6\mathrm{R}}$

3.  $\frac{3\mathrm{V}}{32\mathrm{R}}$

4.  $\frac{3\mathrm{V}}{16\mathrm{R}}$

Two metallic spheres of radii 2cm and 3cm are given charges 6mC and 4mC respectively. The final charge on the smaller sphere will be if they are connected by a conducting wire

1. 4mC

2.6mC

3. 5mC

4. 10mC