A short electric dipole has a dipole moment of \(16 \times 10^{-9} ~\text{C-}\text{m}. \) The electric potential due to the dipole at a point at a distance of \(0.6~\text{m}\) from the centre of the dipole situated on a line making an angle of \(60^{\circ}\) with the dipole axis is:
\(\left( \dfrac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2 \right) \)

An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}.\) The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

An electric dipole with dipole moment \(\vec{p} = \left(3 \hat{i} + 4 \hat{j}\right) \times 10^{- 30}~\text{C-m}\) is placed in an electric field \(\vec{E} = 4000 \hat{i} ~\text{N/C}\). An external agent turns the dipole slowly until its electric dipole moment becomes \(\left(- 4 \hat{i} + 3 \hat{j}\right) \times 10^{- 30}~\text{C-m}\). The work done by the external agent is equal to:
1. \(4\times 10^{-28}~\text{J}\)
2. \(-4\times 10^{-28}~\text{J}\)
3. \(2.8\times 10^{-26}~\text{J}\)
4. \(-2.8\times 10^{-26}~\text{J}\)

An electric dipole of moment \(p\) is placed in an electric field of intensity \(E\). The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ},\) the torque and the potential energy of the dipole will respectively be: