In a parallel plate capacitor of capacitance $C$, a metal sheet is inserted between the plates, parallel to them. If the thickness of the sheet is half of the separation between the plates. The capacitance will be
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A thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $p$ at distance $\frac{R}{2}$ from the centre of the shell is
Consider two charged metallic spheres $S_{1}$ and $\mathrm{S}_{2}$ of radii $\mathrm{R}_{1}$ and $\mathrm{R}_{2},$ respectively. The electric $\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)$ on their surfaces are such that $\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .$ Then the ratio $\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)$ of the electrostatic potentials on each sphere is
The charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in figure. Identify the correct statement$(s)$ related to the $R_1, R_2, C_1 $ and $C_2$ of the two $RC$ circuits.
Three concentric metal shells $A, B$ and $C$ of respective radii $a, b$ and $c (a < b < c)$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is
In a uniform electric field, a cube of side $1\ cm$ is placed. The total energy stored in the cube is $8.85\ \mu J.$ The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is.
The distance between two plates of a capacitor is $d$ and its capacitance is $C _1$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2 d }{3}$ and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes $C _2$. The ratio $\frac{ C _2}{ C _1}$ is:
A parallel plate capacitor has a uniform electric field ' $\overrightarrow{\mathrm{E}}$ ' in the space between the plates. If the distance between the plates is ' $\mathrm{d}$ ' and the area of each plate is ' $A$ ', the energy stored in the capacitor is : $\left(\varepsilon_{0}=\right.$ permittivity of free space)
Charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are a distance $2\,L$ apart, $C$ is the midpoint between $A$ and $B.$ The work done in moving a charge $+Q$ along the semicircle $CRD$ is