The escape speed of an electron launched from the surface of a glass sphere of diameter $1\ cm$ that has been charged to $10\ nC$ is $x \times 10^7\ m/sec$ . The value of $x$ is
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Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area $A$, separated by a distance $d$. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants $K_1$ , $K_2$ and $K_3$ . The first capacitor is filled as shown in fig. $I$, and the second one is filled as shown in fig. $II$. If these two modified capacitors are charged by the same potential $V$, the ratio of the energy stored in the two, would be ( $E_1$ refers to capacitor $(I)$ and $E_2$ to capacitor $(II)$)
An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$
If a point charge $q_A$ is placed at the center of the shell, then choose the correct statement $(s)$
$A$ and $C$ are concentric conducting spherical shells of radius $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric of inner radius $a$, outer radius $b$ and dielectric constant $k$. If sphere $A$ is given a charge $Q$, the potential at the outer surface of the dielectric is.
Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_{1}$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to reduce to one-fourth its initial value. The the ratio $t _{1} / t _{2}$ will be
A capacitor stores $60\ \mu C$ charge when connected across a battery. When the gap between the plates is filled with a dielectric , a charge of $120\ \mu C$ flows through the battery. The dielectric constant of the material inserted is :
An electric dipole is placed as shown in the figure.The electric potential (in $10^2\,V$ ) at point $P$ due to the dipole is $\left(\in_0=\right.$ permittivity of free space and $\left.\frac{1}{4 \pi \in_0}=K\right)$ :
The capacitor of capacitance $C$ in the circuit shown is fully charged initially resistance is $R$. After the switch $S$ is closed, the time taken to reduce the stored energy in the capacitor to half its initial value is
Four identical plates $1, 2, 3$ and $4$ are placed parallel to each other at equal distance as shown in the figure. Plates $1$ and $4$ are joined together and the space between $2$ and $3$ is filled with a dielectric of dielectric constant $k$ $=$ $2$. The capacitance of the system between $1$ and $3$ $\&$ $2$ and $4$ are $C_1$ and $C_2$ respectively. The ratio $\frac{{{C_1}}}{{{C_2}}}$ is