The angle between the electric field and the dipole moment at any point on the equatorial plane of an electric dipole is . . . . . . . (in $^{\circ}$)

Consider a positively charged infinite cylinder with uniform volume charge density. An electric dipole consisting of $+Q$ and $-Q$ charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,

When dipole moment $\vec{P}$ is parallel to a non-uniform electric field $\vec{E}$,the net force on the electric dipole is . . . . . . .

Obtain the equation for the electric field produced by an electric dipole at a point on its equatorial plane.

An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \ C$ separated by a distance of $3 \ cm$ is placed in an electric field of $2 \times 10^5 \ N/C$. The maximum torque on the dipole will be

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