A charged particle $'q'$ is shot from a large distance with speed $v$ towards a fixed  charged particle $Q$. It apporaches $Q$ upto a closet distance $r$ and then returns. If $q$ were given a speed $'2v$', the closest distance of approach would be 

Electric potential at any point is : $V = -5x + 3y + \sqrt {15} z$ ; then the magnitude of electric field is :-

Half of the space between parallel plate capacitor is filled with a medium of dielectric constant $K$ parallel to the plates . If initially the capacity is $C$, then the new capacity will be

There is a square gaussian surface placed in $y-z$ plane. Its axis is along $x-$ axis and centre is at origin. Two identical charges, each $Q$, are placed at point $(a, 0, 0)$ and $(-a, 0, 0)$. Each side length of square is $2a$ then electric flux passing through the square is

A capacitor $C = 100$ $ \mu F$ is connected to three resistors each of resistance $1$ $kW$ and a battery of emf $9$ $V$. The switch $S $ has been closed for long time so as to charge the capacitor. When switch $S $ is opened, the capacitor discharges with time constant…..$ms$