Figures (a) and (b) show the field lines of a positive and negative point charge respectively. The signs of the potential energy difference of a small negative charge between the points Q and P & A and B are respectively:
 

$$\begin{gathered} 1. +, - \\ 2. +, + \\ 3. -, + \\ 4. -, - \end{gathered}$$

Figures (a) and (b) show the field lines of a positive and negative point charge respectively. The sign of the work done by the field in moving a small positive charge from Q to P and the sign of the work done by the external agency in moving a small negative charge from B to A, respectively, will be:
 

$$\begin{gathered} 1. +, - \\ 2. +, + \\ 3. -, + \\ 4. -, - \end{gathered}$$

Figures (a) and (b) show the field lines of a positive and negative point charge respectively. The kinetic energy of a small negative charge in going from B to A:

Four charges are arranged at the corners of a square ABCD of side d, as shown in the figure. The work required to put together this arrangement will be:

$$\begin{gathered} 1. \frac{-q^2}{4\pi {\epsilon }_{0}d}\left(4-\sqrt{2}\right) \\ 2. \frac{-q^2}{4\pi {\epsilon }_{0}d}\left(2-\sqrt{2}\right) \\ 3. \frac{-q^2}{4\pi {\epsilon }_{0}d}\left(4+\sqrt{2}\right) \\ 4. \frac{-q^2}{4\pi {\epsilon }_{0}d}\left(2+\sqrt{2}\right) \end{gathered}$$

Four charges are arranged at the corners of a square ABCD of side d, as shown in the figure. A charge $q_0$ is brought from $\infty$ to the centre E of the square, the four charges being held fixed at its corners. How much work is needed to do this?

$$\begin{gathered} 1. \frac{-{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{d}}\left(4-\sqrt{2}\right) \\ 2. \mathrm{zero} \\ 3. \frac{-{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{d}}\left(4+\sqrt{2}\right) \\ 4. \frac{-{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{d}}\left(2+\sqrt{2}\right) \end{gathered}$$

The electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively is:

How much work is required to separate two charges  7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) infinitely away from each other?

The electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (in an external electric field E = A(1/r²); A = 9 × 10⁵ C m^–2) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively is:

A molecule of a substance has a permanent electric dipole moment of magnitude 10^–29 C m. A mole of this substance is polarised (at low temperature) by applying a strong electrostatic field of magnitude 10⁶ V m^–1. The direction of the field is suddenly changed by an angle of ${60}^0$. The heat released by the substance in aligning its dipoles along the new direction of the field is: (For simplicity, assume 100% polarisation of the sample).

Which one of the following is wrong?

A slab of material of dielectric constant K has the same area as the plates of a parallel-plate capacitor of capacitance $C_0$ but has a thickness (3/4)d, where d is the separation of the plates. What is the capacitance of the capacitor when the slab is inserted between the plates?

$$\begin{gathered} 1. \left(\frac{4\mathrm{K}}{\mathrm{K}+3}\right){\mathrm{C}}_0 \\ 2. \left(\frac{2\mathrm{K}}{\mathrm{K}+2}\right){\mathrm{C}}_0 \\ 3. {\mathrm{C}}_0 \\ 4. \frac{3}{4}{\mathrm{C}}_0 \end{gathered}$$

A network of four 10 µF capacitors is connected to a 500 V supply, as shown in the figure. The equivalent capacitance of the network is:

$$\begin{gathered} 1. \frac{10}{3}\mu F \\ 2. \frac{20}{3}\mu F \\ 3. \frac{40}{3}\mu F \\ 4. \frac{16}{3}\mu F \end{gathered}$$

A network of four 10 µF capacitors is connected to a 500 V supply, as shown in the figure. The charge on the capacitor $\left(C_4\right)$ is: (Note, the charge on a capacitor is the charge on the plate with higher potential, equal and opposite to the charge on the plate with lower potential).

$$\begin{gathered} 1. 1.4\times {10}^{-3} C \\ 2. 9\times {10}^{-4 }C \\ 3. 1.7\times {10}^{-3} C \\ 4. 5.0\times {10}^{-3} C \end{gathered}$$

A 900 pF capacitor is charged by a 100 V battery. The electrostatic energy is stored by the capacitor is U. If the capacitor is disconnected from the battery and connected to another 900 pF capacitor (as shown in the figure ) the electrostatic energy stored by the system is U'. The ratio of $\frac{U}{U\text{'}}$ is:

$$\begin{gathered} 1. \frac{2}{1} \\ 2. \frac{1}{2} \\ 3. 1 \\ 4. \frac{2}{3} \end{gathered}$$

Which of the following is NOT the property of equipotential surface?

An electric dipole of moment p is placed parallel to the uniform electric field. The amount of work done in rotating the dipole by 90⁰ is-

Three capacitors 2µF, 3µF and 6µF are joined in series with each other. The equivalent capacitance is-

A capacitor plates are charged by a battery with ‘V’ volts. After charging battery is disconnected and a dielectric slab with dielectric constant ‘K’ is inserted between its plates, the potential across the plates of a capacitor will become

The equivalent capacitance of the combination shown in the figure is: 

Two charged spherical conductors of radius ${\mathrm{R}}_1 \mathrm{and} {\mathrm{R}}_2$ are connected by a wire. Then the ratio of surface charge densities of the spheres $\left({\mathrm{\sigma }}_1/{\mathrm{\sigma }}_2\right)$ is:

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.