The number of electrons to be put on a spherical conductor of radius $0.1\,m$ to produce an electric field of $0.036\, N/C$ just above its surface is

The bob of a simple pendulum has mass $2\,g$ and a charge of $5.0\,\mu C$. It is at rest in a uniform horizontal electric field of intensity $2000\,\frac{V}{m}$. At equilibrium, the angle that the pendulum makes with the vertical is (take $g = 10\,\frac{m}{{{s^2}}}$)

Four equal positive charges are fixed at the vertices of a square of side $L$. $Z$-axis is perpendicular to the plane of the square. The point $z = 0$ is the point where the diagonals of the square intersect each other. The plot of electric field due to the four charges, as one moves on the $z-$ axis.

A total charge $q$ is divided as $q_1$ and $q_2$ which are kept at two of the vertices of an equilateral triangle of side a. The magnitude of the electric field $E$ at the third vertex of the triangle is to be depicted schematically as a function of $x=q_1 / q$. Choose the correct figure.

The tiny ball at the end of the thread shown in figure has a mass of $0.5 \, g$ and is  placed in a horizontal electric field of intensity $500\, N/C$. It is in equilibrium in the  position shown. The magnitude and sign of the charge on the ball is .....$\mu C$

Five point charge each having magnitude $‘q’$ are placed at the corner of hexagon as shown in fig. Net electric field at the centre $‘O’$ is $\vec E$. To get net electric field at $‘O’$ be $6\vec E$, charge placed on the remaining sixth corner should be