Five equal point charges with Q = 10 nC are located at x = 2, 4, 5, 1 O and 20 m. If ε₀ = [10^-9 / 36π] F/m, then the potential at the origin (x = O) is

• 9.9 V

• 11.1 V

• 90 V

• 99 V

The force between two point charges placed in a material medium of dielectric constant ε_r is F. If the material is removed, then the force between them becomes

• ε_rF

• εF

• $\frac{\mathrm{F}}{{\mathrm{\epsilon }}_{\mathrm{r}}}$

• $\frac{\mathrm{\epsilon }}{\mathrm{F}}$

A conductor with a cavity is charged positively and its surface charge density is σ. If E and Vrepresent the electric field and potential, then inside the cavity

• and V = 0

• E = 0 and V = 0

• E = 0 and V = constant

• V = 0 and σ = constant

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

• $\mathrm{Q} \left(\frac{\mathrm{a} + \mathrm{b}}{{\mathrm{a}}^2 + {\mathrm{b}}^2}\right)$

• $2\mathrm{Q} \left(\frac{\mathrm{a} + \mathrm{b}}{{\mathrm{a}}^2 + {\mathrm{b}}^2}\right)$

• Q

• $\frac{\mathrm{Q}}{2} \left(\frac{\mathrm{a} + \mathrm{b}}{{\mathrm{a}}^2 + {\mathrm{b}}^2}\right)$

A 5 µF capacitor is fully charged by a 12 V battery and then disconnected. If it is connected now parallel to an uncharged capacitor, the voltage across it is 3 V. Then, the capacity of the uncharged capacitor is

• 5 µF

• 25 µF

• 50 µF

• 10 µF

In the given circuit below, the points A, B and C are at same potential. If the potential difference between B and D is 30 V, then the potential difference between A and O is

• 7.5 V

• 10 V

• 15 V

• 5 V

The energy stored in a capacitor of capacitance C having a charge Q under a potential V is

• $\frac{1}{2}{\mathrm{Q}}^2\mathrm{V}$

• $\frac{1}{2} {\mathrm{C}}^2\mathrm{V}$

• $\frac{1}{2} \frac{{\mathrm{Q}}^2}{\mathrm{V}}$

• $\frac{1}{2} \mathrm{QV}$

The electrostatic force between two point charges is directly proportional to the

• sum of the charges

• distance between the charges

• product of the charges

• permittivity of the medium

A point charge of 2 C experiences a constant force of 1000 N when moved between two points separated by a distance of 2 cm in a uniform electric field. The potential difference between the two points is

• 12 V

• 8 V

• 10 V

• 16 V

An uncharged parallel plate capacitor filled with a dielectric of dielectric constant K is connected to an air filled identical parallel capacitor charged to potential V₁. If the common potential is V₂, the value of K is

• $\frac{{\mathrm{V}}_1 - {\mathrm{V}}_2}{{\mathrm{V}}_1}$

• $\frac{{\mathrm{V}}_1}{{\mathrm{V}}_1 - {\mathrm{V}}_2}$

• $\frac{{\mathrm{V}}_2}{{\mathrm{V}}_1 - {\mathrm{V}}_2}$

• $\frac{{\mathrm{V}}_1 - {\mathrm{V}}_2}{{\mathrm{V}}_2}$