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

Four equal charges Q are placed at the four corners of a square of each side is ‘a’. Work done in removing a charge – Q from its centre to infinity is 

(1) 0

(2) $\frac{\sqrt{2}{Q}^2}{4\pi {\epsilon }_{0}a}$

(3) $\frac{\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$

(4) $\frac{Q^2}{2\pi {\epsilon }_{0}a}$

100 capacitors each having a capacity of 10 μF are connected in parallel and are charged by a potential difference of 100 kV. The energy stored in the capacitors and the cost of charging them, if electrical energy costs 108 paise per kWh, will be 

(1) 10⁷ joule and 300 paise

(2) 5 × 10⁶ joule and 300 paise

(3) 5 × 10⁶ joule and 150 paise

(4) 10⁷ joule and 150 paise

Two identical metal plates are given charges $Q_1 and Q_2\left(<Q_1\right)$ respectively. If they are now brought close to form a parallel plate capacitor with capacitance $C$, the potential difference between them is :

1. $\frac{Q_1+Q_2}{2C}$

2. $\frac{Q_1+Q_2}{C}$

3. $\frac{Q_1-Q_2}{C}$

4. $\frac{Q_1-Q_2}{2C}$