In infinite long uniformly charged string is placed along $z-$ axis. Its linear charge density is $\lambda $. A point charge $q$ is moved from position $(a, 0, 0)$ to $(2a, 0, 0)$ then work done will be
$ - \frac{{K\lambda }}{a}\left( q \right)$
$\frac{{K\lambda q}}{{2a}}\,\ln \,\left( 2 \right)$
$ - 2k\lambda q\,(\ln \,2)$
$ - \frac{{2k\lambda q}}{a}\,(\ln \,2)$
Find capacitance across $AB$
A charge $Q$ is distributed over two concentric hollow spheres or radius $r$ and $R(> r)$ such that the surface densities are equal. The potential at the common centre is
The equivalent capacitance between points $A$ and $B$ of the circuit shown will be
A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A$ , the energy stored in the capacitor is
The plates of a parallel plate capacitor are charged up to $100\, volt$ . A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$ . The dielectric constant of the plate is