An electric dipole consisting of two opposite charges of $2 \times 10^{-6} \ C$ separated by a distance of $3 \ cm$ is placed in an electric field of $2 \times 10^5 \ N/C$. The maximum torque on the dipole will be

Write the equation for the electric field produced by an electric dipole at a point on its axial line,given the condition $r >> a$.

An electric dipole in a uniform electric field experiences (when it is placed at an angle $\theta$ with the field):

In a certain region of space,the electric field is along the $z$-direction throughout. The magnitude of the electric field is,however,not constant but increases uniformly along the positive $z$-direction at the rate of $10^{5} \; N \, C^{-1}$ per meter. What are the force and torque experienced by a system having a total dipole moment equal to $10^{-7} \; C \, m$ in the negative $z$-direction?

An electric field of $1000\,V/m$ is applied to an electric dipole at an angle of $45^\circ$. The value of the electric dipole moment is $10^{-29}\,C\cdot m$. What is the potential energy of the electric dipole?

An electric dipole of dipole moment $p$ is aligned parallel to a uniform electric field $E$. The energy required to rotate the dipole by $90^{\circ}$ is $\left[\begin{array}{ll}\sin 0^{\circ}=0, & \sin 90^{\circ}=1 \\ \cos 0^{\circ}=1, & \cos 90^{\circ}=0\end{array}\right]$