An electric dipole having each charge of magnitude $2 \mu C$ is placed in an electric field of intensity $8 \times 10^{4} \ N/C$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \ N \cdot m$,the length of the dipole is: (in $mm$)

Two charges $+q$ and $-q$ are kept at a certain distance apart. Then, at any point on the perpendicular bisector of the line joining the two charges:

An electric dipole of dipole moment $\vec{P}$ is placed parallel to a uniform electric field of intensity $\vec{E}$. On rotating it through $180^{\circ}$,the amount of work done is . . . . . . .

An electric dipole of moment $\vec{P}$ is placed in a uniform electric field $\vec{E}$ such that $\vec{P}$ points along $\vec{E}$. If the dipole is slightly rotated about an axis perpendicular to the plane containing $\vec{E}$ and $\vec{P}$ and passing through the centre of the dipole, the dipole executes simple harmonic motion. Consider $I$ to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation?

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

$A$ neutral water molecule $(H_2O)$ in its vapor state has an electric dipole moment of magnitude $6.4 \times 10^{-30} \ C \cdot m$. How far apart are the molecule's centers of positive and negative charge?