The electric field at the equator of a dipole is \(E.\) If the strength of the dipole and distance are now doubled, then the electric field will be:

A point \(Q\) lies on the perpendicular bisector of an electric dipole of dipole moment \(p.\) If the distance of \(Q\) from the dipole is \(r\) (much larger than the size of the dipole), then the electric field at \(Q\) is proportional to:
1. \(p^{2}\) and \(r^{-3}\)
2. \(p\) and \(r^{-2}\)
3. \(p^{-1}\) and \(r^{-2}\)
4. \(p\) and \(r^{-3}\)

A dipole of moment $\overrightarrow{p}$ is placed in uniform electric field $\overrightarrow{E}$. The torque acting on it is given by:
1. \(\vec{\tau }=\vec{p}.\vec{E}\)
2. \(\vec{\tau }=\vec{p} \times\vec{E}\)
3. \(\vec{\tau }=\vec{p}+\vec{E}\)
4. \(\vec{\tau }=\vec{p}-\vec{E}\)