An electric dipole having a dipole moment of 4.0 10⁻⁶ C m and a moment of inertia of 4.0 10⁻⁴ kg m ^2 is held at an angle of 90^ to a uniform electric field of 2.0 10^4 N/C. If the dipole is released from rest, its maximum angular speed will be _______ rad/s.

Step-by-step solution

When the dipole is released, the electric torque will rotate it towards the stable equilibrium position ( = 0^ ). The angular speed will be maximum when the potential energy is minimum, which occurs at = 0^ . By conservation of mechanical energy: K + U = 0 K_f - K_i + U_f - U_i = 0 Initial state (at rest): K_i = 0 U_i = -pE 90^ = 0 Final state (at maximum speed): K_f = 1 2 I ^2 U_f = -pE 0^ = -pE Substituting these into the energy conservation equation: 1 2 I ^2 - pE = 0 1 2 I ^2 = pE Given values: p = 4.0 10⁻⁶ C m