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

A finite ladder is constructed by connecting several sections of 2 μF, 4 μF capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance C. What value should be chosen for C such that the equivalent capacitance of the ladder between the points A and B becomes independent of the number of sections in between 

(1) 4 μF

(2) 2 μF

(3) 18 μF

(4) 6 μF

The insulated spheres of radii R₁ and R₂ having charges Q₁ and Q₂ respectively are connected to each other. There is -

(1) No change in the energy of the system

(2) An increase in the energy of the system

(3) Always a decrease in the energy of the system

(4) A decrease in the energy of the system unless Q₁R₂ = Q₂R₁

A capacitor of 2$\mu F$ is charged as shown in the figure. When the switch S is turned to position 2, the percentage of its stored energy dissipated is

1. 20%               2. 75%

3. 80%               4. 0%

Four charges $+Q,-Q,+Q,-Q$ are placed at the corners of a square taken in order. At the centre of the square 

(1) $E=0,V=0$

(2) $E=0,V\ne 0$

(3) $E\ne 0,V=0$

(4) $E=0,V\ne 0$

A charge $\mathrm{Q}$ is distributed over two concentric hollow spheres of radii r and $\mathrm{R} \left(\mathrm{R} > \mathrm{r}\right)$ such that the surface densities are equal. The potential at the common centre is $\frac{1}{4{\mathrm{\pi \epsilon }}_0}$ times –

1.  $\mathrm{Q} \left(\frac{\mathrm{r}+\mathrm{R}}{{\mathrm{r}}^2+{\mathrm{R}}^2}\right)$                       

2.  $\frac{\mathrm{Q}}{2} \left(\frac{\mathrm{r}+\mathrm{R}}{{\mathrm{r}}^2+{\mathrm{R}}^2}\right)$

3.  $2\mathrm{Q} \left(\frac{\mathrm{r}+\mathrm{R}}{{\mathrm{r}}^2+{\mathrm{R}}^2}\right)$                     

4.  Zero

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles, then 

(1) The charge on the capacitor increases

(2) The voltage across the plates decreases

(3) The capacitance increases

(4) The electrostatic energy stored in the capacitor increases

Electric potential is given by

$V=6x-8x{y}^2-8y+6yz-4z^2$

Then electric force acting on 2C point charge placed on origin will be 

(1) 2N

(2) 6N

(3) 8N

(4) 20N

A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V₀. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is 

(1) $\frac{3{\epsilon }_{0}A{V}_0^2}{d}$

(2) $\frac{{\epsilon }_{0}A{V}_0^2}{2d}$

(3) $\frac{{\epsilon }_{0}A{V}_0^2}{3d}$

(4) $\frac{{\epsilon }_{0}A{V}_0^2}{d}$