Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is
$4\pi {\varepsilon _0}\frac{{ab}}{{b - a}}$
$4\pi {\varepsilon _0}(a + b)$
$4\pi {\varepsilon _0}b$
$4\pi {\varepsilon _0}a$
Capacitance (in $F$) of a spherical conductor with radius $1\, m$ is
The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor
Two identical thin metal plates has charge $q _{1}$ and $q _{2}$ respectively such that $q _{1}> q _{2}$. The plates were brought close to each other to form a parallel plate capacitor of capacitance $C$. The potential difference between them is.
A small sphere carrying a charge ‘$q$’ is hanging in between two parallel plates by a string of length $L$. Time period of pendulum is ${T_0}$. When parallel plates are charged, the time period changes to $T$. The ratio $T/{T_0}$ is equal to
Two metal spheres of capacitance ${C_1}$ and ${C_2}$ carry some charges. They are put in contact and then separated. The final charges ${Q_1}$ and ${Q_2}$ on them will satisfy