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Three point charges $Q, 4Q $ and $16Q $ are placed on a straight line $9$ $cm$ long. Charges are placed in such a way that the system has minimum potential energy. Then
A parallel plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constants ${k_1},{k_2}$ and ${k_3}$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by
As shown in figure, on bringing a charge $Q$ from point $A$ to $B$ and from $B$ to $C$, the work done are $2\, joule$ and $-3\, joule$ respectively. The work done to bring the charge from $C$ to $A$ is
Two charges of $4\,\mu C$ each are placed at the corners $A$ and $B $ of an equilateral triangle of side length $0.2\, m $ in air. The electric potential at $C$ is $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N{\rm{ - }}{m^2}}}{{{C^2}}}} \right]$
Two points $P$ and $Q$ are maintained at the potentials of $10\, V$ and $-4\,V$, respectively. The work done in moving $100$ electrons from $P$ and $Q$ is
A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is
A parallel plate capacitor with air between plates has a capacitance of $8\,\mu F$ what will be capacitance if distance between plates is reduced by half, and the space between them is filled with a substance of dielectric constant $6$ ?.....$\mu F$