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 $g = 10\,\frac{m}{{{s^2}}}$)

As shown in the figure, a particle A of mass $2\,m$ and carrying charge $q$ is connected by a light rigid rod of length $L$ to another particle $B$ of mass $m$ and carrying charge $-q.$ The system is placed in an electric field $\vec E$ . The electric force on a charge $q$ in an electric field $\vec E$ is $\vec F = q \vec E $ . After the system settles into equilibrium, one particle is given a small push in the transverse direction so that the rod makes a small angle $\theta_0$ with the electric field. Find maximum tension in the rod.

A charged particle of mass $5 \times {10^{ - 5}}\,kg$ is held stationary in space by placing it in an electric field of strength ${10^7}\,N{C^{ - 1}}$ directed vertically downwards. The charge on the particle is

A hollow sphere of charge does not produce an electric field at any

Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness $k$ is $T$. When block is uncharged. If a charge $q$ is given to the block them, the new time period of oscillation will be

Four point charges $-q, +q, +q$ and $-q$ are placed on $y$ axis at $y = -2d$, $y = -d, y = +d$ and $y = +2d$, respectively. The magnitude of the electric field $E$ at a point on the $x -$ axis at $x = D$, with $D > > d$, will vary as