A simple pendulum of length $l$ has a bob of mass $m$ ，with a charge $q$ ．On it a vertical sheet of charge， with surface charge density＇$\sigma$＇passes through the point of suspension．At equilibrium，if the string makes an angle $\theta$ with the vertical，then

Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field $E(t)=E_0 \sin \omega t$ in the $x$-direction, where $E_0=2$ Newton/Coulomb and $\omega=1000 \mathrm{rad} / \mathrm{sec}$. The maximum speed attained by the particle is

Two charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance $2 L_{\mathrm{p} p a t}$ $C$ is the mid point of $A$ and $B$. The workdone in moving a charge $+Q$ along the semicircle $\operatorname{CSD}\left(W_V\right)$ and along the line $\mathrm{CBD}\left(W_2\right)$ are

A charge Q is placed at the centre of a cube of sides a. The total flux of electric field through the six surfaces of the cube is