A uniformly charged rod of length $4\,m$ and linear charge density $\lambda  = 30\,\mu C/m$ is placed as shown in figure. Calculate the $x-$ component of electric field at point $P$.

A drop of ${10^{ - 6}}\,kg$ water carries ${10^{ - 6}}\,C$ charge. What electric field should be applied to balance its weight (assume $g = 10\,m/{s^2}$)

An infinite number of electric charges each equal to $5\, nC$ (magnitude) are placed along $X$-axis at $x = 1$ $cm$, $x = 2$ $cm$ , $x = 4$ $cm$ $x = 8$ $cm$ ………. and so on. In the setup if the consecutive charges have opposite sign, then the electric field in Newton/Coulomb at $x = 0$ is $\left( {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,N - {m^2}/{c^2}} \right)$

$(a)$ Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where $E =0$ ) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

$(b)$ Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

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 $g = 10\,\frac{m}{{{s^2}}}$)

The electric field in a region is radially outward and at a point is given by $E=250 \,r V / m$ (where $r$ is the distance of the point from origin). Calculate the charge contained in a sphere of radius $20 \,cm$ centred at the origin ......... $C$