Two electric dipoles of moment $P$ and $64 P$ are placed in opposite directions on a line at a distance of $25 \ cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $P$ is.....$cm$.

Electric field at the equator of a dipole is $E$. If both dipole moment and distance are doubled,then the electric field will be $:-$

One end of a spring of negligible unstretched length and spring constant $k$ is fixed at the origin $(0,0)$. $A$ point particle of mass $m$ carrying a positive charge $q$ is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\overrightarrow{p}$ pointing towards the charge $q$ is fixed at the origin,the spring gets stretched to a length $\ell$ and attains a new equilibrium position. If the point mass is now displaced slightly by $\Delta \ell \ll \ell$ from its equilibrium position and released,it is found to oscillate at frequency $\frac{1}{\delta} \sqrt{\frac{k}{m}}$. The value of $\delta$ is. . . . . .

$A$ point particle of mass $M$ is attached to one end of a massless non-conducting rod of length $L$. Another point particle of the same mass is attached to the other end of the rod. The two particles carry charges $+q$ and $-q$ respectively. This arrangement is placed in a region of uniform electric field $E$. When the rod makes a small angle $(< 5^o)$ with the direction of the field,what is the minimum time required for the rod to become parallel to the field?

Two point dipoles $p \hat{k}$ and $\frac{p}{2} \hat{k}$ are located at $(0, 0, 0)$ and $(1 \text{ m}, 0, 2 \text{ m})$ respectively. The resultant electric field due to the two dipoles at the point $(1 \text{ m}, 0, 0)$ is

Two tiny electric dipoles of dipole moments $P_1$ and $P_2$ are placed at a distance $r$ coaxially. Find the magnitude of the electrostatic force between them.