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A frictionless dielectric plate $S$ is kept on a frictionless table $T$. A charged parallel plate capacitance $C$ (of which the plates are frictionless) is kept near it. The plate $S$ is between the plates. When the plate $S$ is left between the plates
. Three identical capacitors $C _1, C _2$ and $C _3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C _1$ is then filled completely with a dielectric material of relative permittivity $\varepsilon_{ r }$. The cell electromotive force (emf) $V_0=8 V$. First the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged, $S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium, the charge on $C _3$ is found to be $5 \mu C$. The value of $\varepsilon_{ r }=$. . . . .
A cylindrical capacitor has two co-axial cylinders of length $20 \,cm$ and radii $2 r$ and $r$. Inner cylinder is given a charge $10 \,\mu C$ and outer cylinder a charge of $-10 \,\mu C$. The potential difference between the two cylinders will be
Two condensers of capacity $0.3\,\mu F$ and $0.6\,\mu F$ respectively are connected in series. The combination is connected across a potential of $6\,volts$. The ratio of energies stored by the condensers will be
An electric dipole moment $\vec p = (2.0\hat i + 3.0\hat j)$ $\mu C. $ $m$ is placed in a uniform electric field $\vec E = (3.0\hat i + 2.0\hat k)$ $×$$10^5$ $N$ $C^{-1}$.
A point charge $q$ is held at the centre of a circle of radius $r . B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{A B}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{A C}$ represents the workdone from $A$ to $C$, then
The dielectric strength of air at $NTP$ is $3 \times {10^6}\,V/m$ then the maximum charge that can be given to a spherical conductor of radius $3\, m$ is