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)$
A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$ . The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is
An electric dipole of dipole moment $\vec P$ is lying along a uniform electric field $\vec E$ . The work done in rotating the dipole by $90^o$ is
A sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$ whose centre coincides with the given sphere. The flux related to imaginary sphere is
What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line.......$^o$
Five balls marked a to $e$ are suspended using separate threads. Pairs $(b, c)$ and $(d, e)$ show electrostatic repulsion while pairs $(a, b),(c, e)$ and $(a, e)$ show electrostatic attraction. The ball marked a must be