$A$ wheel of mass $m$ has charges $+q$ and $-q$ at diametrically opposite points. It remains in equilibrium on a rough inclined plane of inclination $\theta$ in the presence of a uniform horizontal electric field $E$. Find the value of $E$.

An electrical dipole coincides on the $z$-axis and its midpoint is at the origin of the coordinate system. The electric field at an axial point at a distance $z$ from the origin is $\vec{E}(z)$ and the electric field at an equatorial point at a distance $y$ from the origin is $\vec{E}(y)$. Here $z = y \gg a$,so $\left| \frac{\vec{E}(z)}{\vec{E}(y)} \right| = . . . . . . . .$.

The distance between charges $+q$ and $-q$ is $2l$ and between $+2q$ and $-2q$ is $4l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha \left[ \frac{ql}{r^2} \right] \times 10^9 \text{ V}$,where the value of $\alpha$ is . . . . . . . (Use $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \text{ Nm}^2\text{C}^{-2}$)

The electric field at a point on the equatorial plane at a distance $r$ from the centre of a dipole having dipole moment $\overrightarrow{p}$ is given by,($r >>$ separation of two charges forming the dipole,$\varepsilon_{0}$ - permittivity of free space)

When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole,the work done is ..........

Three point charges $+q$,$-2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0)$,$(x = 0, y = 0, z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are