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 the surface of a charged solid sphere of insulator is \(20\text{ V}.\) The value of electric potential at its centre will be

1.  \(30\text{ V}\)

2.  \(20\text{ V}\)

3.  \(40\text{ V}\)

4.  Zero

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

A and B are two concentric metallic shells. If A is positively charged and B is earthed, then electric

1.  Field at common centre is non-zero

2.  Field outside B is nonzero

3.  Potential outside B is positive

4.  Potential at common centre is positive

Two spheres of radius a and b respectively are charged and joined by a wire. The ratio of the electric field at the surface of the spheres is 

(1) a/b

(2) b/a

(3) a²/b²

(4) b²/a²