The capacity of a parallel plate capacitor of each plate area of $10cm \times 10cm$ and separated by a distance 1 mm

$C = \frac{{{ \in _0}A}}{d} = \frac{{8.85 \times {{10}^{ - 12}} \times 10 \times {{10}^{ - 2}} \times 10 \times {{10}^{ - 2}}}}{{1 \times {{10}^{ - 3}}}}$ $C = 8.85 \times {10^{ - 11}}F$ $ = 8.85 \times {10^{ - 12}}F = 88.5PF$

The correct Option is "$88.42\,PF$"

A charge “$Q$ ” is placed at each other corner of a cube of side “$a$ ”. The potential at the centre of cube is

$V = \frac{1}{{4\pi {\varepsilon _0}}}.\frac{q}{d}$

$\frac{{8Q}}{{\pi {\varepsilon _0}a}}$

$\frac{{4Q}}{{4\pi {\varepsilon _0}a}}$

The correct Option is "$\frac{{4Q}}{{\sqrt 3 \pi {\varepsilon _0}a}}$"

$\frac{{2Q}}{{\pi {\varepsilon _0}a}}$

A half ring of radius $R$ has a charge of $\lambda $ per unit length. The potential at the centre of the half ring is $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

$q = \lambda \pi r\,\,{\rm{and}}\,\,V = \frac{{kq}}{r}$

The correct Option is "$K\pi \lambda $"

A uniform electric field pointing in positive x-direction exists in a region let $A$ be the origin $B$ be the point on x-axis at $x = + 1\,cm$ and $C$ be the point on y-axis at $y = + 1\,cm$. Then the potentials at points A,B, and C satisfy.

Alone the field direction potential decreases

The correct Option is "${V_A} > {V_B}$"

The electric field at origin is along the $ + ve$ x-axis. A mall circle is drawn with the centre at origin cutting the axes at the points A,B,C and D having coordinates $\left( {a,0} \right),\left( {0,a} \right),\left( { - a,0} \right),\left( {0, - a} \right)$ respectively. Out of the points on the periphery of the circle, the potential is minimum at .

$V = - \overrightarrow E .d\overrightarrow r $

The capacity of a parallel plate condenser consisting of two plates each 20 cm square and are separated by a distance of 8 mm is (Take air as the medium between the plates).

$C = \frac{{{\varepsilon _0}A}}{d}$

The correct Option is "$2.2 \times {10^{ - 12}}F$"

Twenty seven spherical drops each of radius 2 cm and carrying 5 C charge combine to form a bigger drop. Its capacity is.

The correct Option is "$\frac{6}{9} \times {10^{ - 11}}F$"

A parallel plate condenser has initially air medium between the plates. If a slab of dielectric constant 10 having thickness half the distance of separation between the plates is introduced, the percentage increase in its capacity is

${C_0} = \frac{{{\varepsilon _0}A}}{d};C = \frac{{{\varepsilon _0}A}}{{d - t\left( {1 - \frac{1}{K}} \right)}}$ $\Delta C\,\% = \frac{{C - {C_0}}}{{{C_0}}} \times 100\,\% $

The correct Option is "$81.8{\rm{ }}\% $"

Polar molecules are the molecules

In polar molecules, the centre of positive charges does not coincide with the centre of negative charges. Hence, these molecules have a permanent electric dipole moment of their own.

Acquire a dipole moment only when magnetic field is absent

The correct Option is "Having a permanent electric dipole moment"

Acquire a dipole moment only in the presence of electric field due to displacement of charges

Two charged spherical conductors of radius ${R_1}{\rm{ and }}{R_2}$ are connected by a wire. Then the ratio of surface charge densities of the spheres $({\sigma _1}/{\sigma _2})$ is

When two conductors are connected by a conducting wire, then the two conductors should have same potential. So, ${V_1} = {V_2}$ $\begin{array}{*{20}{l}} {\therefore \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}}}{{{R_1}}} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_2}}}{{{R_2}}}}\\ { \Rightarrow \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_1}}}{{{R_1}}} \times \frac{{{R_1}}}{{{R_1}}} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q_2}}}{{{R_2}}} \times \frac{{{R_2}}}{{{R_2}}}}\\ { \Rightarrow \frac{{{Q_1}{R_1}}}{{4\pi R_1^2{\varepsilon _0}}} = \frac{{{Q_2}{R_2}}}{{4\pi R_2^2{\varepsilon _0}}}}\\ { \Rightarrow \frac{{{\sigma _1}{R_1}}}{{{\varepsilon _0}}} = \frac{{{\sigma _2}{R_2}}}{{{\varepsilon _0}}}}\\ { \Rightarrow \frac{{{\sigma _1}}}{{{\sigma _2}}} = \frac{{{R_2}}}{{{R_1}}}} \end{array}$