Formula: Electric Dipole Torque Electric field (E field) Electric dipole moment Angle
$$\class{green}{M} ~=~ \class{purple}{E} \, d \, \sin(\varphi)$$
$$\class{green}{M} ~=~ \class{purple}{E} \, d \, \sin(\varphi)$$
$$\class{purple}{E} ~=~ \frac{\class{green}{M}}{ d \, \sin(\varphi) }$$
$$d ~=~ \frac{\class{green}{M}}{ \class{purple}{E} \, \sin(\varphi) }$$
$$\varphi ~=~ \arcsin\left( \frac{ \class{green}{M} }{ \class{purple}{E} \, d } \right)$$
Torque
$$ \class{green}{M} $$ Unit $$ \mathrm{Nm} = \frac{\mathrm{kg} \, \mathrm{m}^2}{\mathrm{s}^2} $$
Magnitude of the torque experienced by an electric dipole in an external (homogeneous) electric field. The dipole is aligned along the electric field lines.
E-field
$$ \class{purple}{\boldsymbol E} $$ Unit $$ \frac{\mathrm{V}}{\mathrm{m}} = \frac{\mathrm{N}}{\mathrm{C}} = \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{A} \, \mathrm{s}^3} $$
External (homogeneous) electric field in which the electric dipole is placed.
Dipole moment
$$ \boldsymbol{d} $$ Unit $$ \mathrm{Cm} $$
Electrical dipole moment of two oppositely charged point charges \(+q\) and \(-q\), which are at a distance \( \boldsymbol{r} \) to each other. The larger the charge and the greater the distance between the charge carriers, the greater the electric dipole moment.
Angle
$$ \varphi $$ Unit $$ \mathrm{rad} = 1 $$
Angle between the dipole moment vector (longitudinal axis of the dipole) and the E-field vector (electric field lines).