51.

N identical drops of mercury are charged sumultaneously to 10 V. When combined to form one large drop, the potential is found to be 40 V, the value of N is

• 4

• 6

• 8

• 10

The electrostatic potential energy between proton and electron separated by a distance 1 $\stackrel{\circ }{\mathrm{A}}$ is

• 13.6 V

• 27.2 eV

• 14.4 eV

• 1.44 eV

The plates of a parallel plate capacitor with air as medium are separated by a distance of 8 mm. A medium of dielectric constant 2 and thickness 4 mm having the same area is introduced between the plates. For the capacitance to remain the same, the distance between the plates is

• 8 mm

• 6 mm

• 10 mm

• 12 mm

Two identical air core capacitors are connected in series to a voltage source of 15 V. If one of the capacitors is filled with a medium of dielectric constant 4, the new potential across this capacitor is

• 5 V

• 8 V

• 10 V

• 12 V

A network of six identical capacitors, each of value C, is made as shown in the figure.

The equivalent capacitance between the points A and B is

• $\frac{4\mathrm{C}}{11}$

• 3C/4

• 3C/2

• 3C

Find the potential at the centre of a square of side $\sqrt{2}$ m which carries at its four corners charges q₁ = 3 × 10^-6 C, q₂ = − 3 × 10^-6 C, q₃ = − 4 × 10^-6 C, q₄ = 7 × 10^-6 C

• 2.7 × 10⁴ V

• 1.5 × 10³ V

• 3 × 10² V

• 5 × 10³ V

If c is the speed of electromagnetic waves in vacuum, its speed in a medium of dielectric constant K and relative permeability μ_r is

• $\mathrm{v} = \frac{1}{\sqrt{{\mathrm{\mu }}_{\mathrm{r}}\mathrm{K}}}$

• $\mathrm{v} = \mathrm{c}\sqrt{{\mathrm{\mu }}_{\mathrm{r}}\mathrm{K}}$

• $\mathrm{v} = \frac{\mathrm{c}}{\sqrt{{\mathrm{\mu }}_{\mathrm{r}}\mathrm{K}}}$

• $\mathrm{v} = \frac{\mathrm{K}}{\sqrt{{\mathrm{\mu }}_{\mathrm{r}}\mathrm{c}}}$

The electrostatic field due to a charged conductor just outside the conductor is

• zero and parallel to the surface at every point inside the conductor

• zero and is normal to the surface at every point inside the conductor

• parallel to the surface at every point and zero inside the conductor

• normal to the surface at every point and zero inside the conductor

Figure below shows four plates each of area A and separated from one another by a distance d. What is the capacitance between P and Q ?

• $\frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

• $\frac{2{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

• $\frac{3{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

• $\frac{4{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

A soap bubble is charged to a potential of 16 V. Its radius is, then doubled. The potential of the bubble now will be

• 16 V

• 8 V

• 4 V

• 2 V