Two electric charges $+2 \mu C$ and $-4 \mu C$ are separated by a distance $3 \ m$ in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at point $P$ (in $NC^{-1}$) is (in $,000$)

Two identical charges $+Q$ are kept fixed at some distance apart. $A$ small particle $P$ with charge $q$ is placed midway between them. If $P$ is given a small displacement $\Delta$,it will undergo simple harmonic motion if:

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path of radius $r$,the work done will be equal to

Six infinitely large and thin non-conducting sheets are fixed in configurations $I$ and $II$. As shown in the figure,the sheets carry uniform surface charge densities which are indicated in terms of $\sigma_0$. The separation between any two consecutive sheets is $d = 1 \mu m$. The various regions between the sheets are denoted as $1, 2, 3, 4$ and $5$. If $\sigma_0 = 9 \mu C / m^2$,then which of the following statements is/are correct: (Take permittivity of free space $\epsilon_0 = 9 \times 10^{-12} F / m$):

As shown in the figure,a point charge $q_{1} = +1 \times 10^{-8} \ C$ is placed at the origin in the $x-y$ plane and another point charge $q_{2} = +3 \times 10^{-6} \ C$ is placed at the coordinate $(10, 0)$. In that case,which of the following graph$(s)$ shows most correctly the electric field vector $E_{x}$ in the $x$-direction?

$A$ particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle loses contact with the sphere when the line joining the center of the sphere and the particle makes an angle $45^{\circ}$ with the vertical. The ratio $\frac{qE}{mg}$ is: