$A$ 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 $E$.

Two short dipoles $A$ and $B$, $A$ having charges $\pm 2 \mu C$ and length $1 \text{ cm}$, and $B$ having charges $\pm 4 \mu C$ and length $1 \text{ cm}$, are placed with their centres $80 \text{ cm}$ apart as shown in the figure. The electric field at a point $P$, equidistant from the centres of both dipoles, is . . . . . . $\text{N/C}$.

An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole is zero when $\theta = 90^o$,the torque and the potential energy of the dipole will respectively be

From which law and principle can the electric field of an electric dipole be obtained?

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 $\left| \frac{\vec{E}(z)}{\vec{E}(y)} \right| = . . . . . . . .$.

An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $60^{\circ}$ with a uniform electric field. It experiences a torque of $4 \sqrt{3} \ Nm$. Calculate the magnitude of the electric field. (The dipole has charges $\pm 8 \ nC$)