The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A is:

The diagrams below show regions of equipotentials.

A positive charge is moved from A to B in each diagram. Then:

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system:-

1. Decreases by a factor of 2

2. Remains the same

3. Increases by a factor of 2

4. Increases by a factor of 4

An electric dipole is place at an angle of \(30^{\circ}\) with an electric field intensity \(2\times10^{5}~\text{N/C}\). It experiences a torque equal to \(4~\text{Nm}\). The charge on the dipole, if the dipole length is \(2~\text{cm}\), is: 

A parallel-plate capacitor of area A, plate separation d, and capacitance C is filled with four dielectric materials having dielectric constants $k_1,k_2,k_3$ $$and $k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

(a) $\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

(b) $k=\frac{2}{3}\left(k_1+k_2+k_3\right)+2k_4$

(c) $\frac{1}{k}=\frac{3}{2\left(k_1+k_2+k_3\right)}+\frac{1}{2k_4}$

(d) $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

A capacitor of \(2\) µF is charged as shown in the figure. When the switch \(\mathrm{S}\) is turned to position \(2,\), the percentage of its stored energy dissipated is:

   

1. \(20\)%
2. \(75\)%
3. \(80\)%
4. \(0\)%