The magnitude of the charge of an electric dipole is $3.2 \times 10^{-19} \ C$ and the distance between them is $2.4 \ \mathring{A}$. If it is placed in an electric field of $4 \times 10^5 \ V/m$,then its dipole moment (in $C-m$) is .......

The figure shows an electric field in which an electric dipole $\overrightarrow{P}$ is placed. Which of the following statements is correct?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: If an electric dipole of dipole moment $30 \times 10^{-5} \, Cm$ is enclosed by a closed surface,the net flux coming out of the surface will be zero.
Reason $R$: An electric dipole consists of two equal and opposite charges.
In the light of the above statements,choose the correct answer from the options given below:

If $E_{a}$ and $E_{q}$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance $r$ from the centre of the dipole,then

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. . . . . .

An electric dipole consists of two opposite charges each of magnitude $1 \,\mu C$ separated by a distance of $2 \,cm$. The dipole is placed in an external field of $10^5 \,N/C$. The maximum torque on the dipole is ......... $Nm$.