Question

(c) An electric dipole consists of 1.0 g spheres charged to +3.0nC at the ends of a 15 cm long non-conducting rod of mass 4g (don't try to look up "electric dipole", it won't help you. For the sake of this problem, it's just a fancy word for what I just described). The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular to a uniform electric field with a field strength 1000 V/m, then released. What is the dipole's angular velocity at the instant it is aligned with the electric field? (HINT: Look up the moment of inertia of the rotating rod about its center and don't forget the rotational kinetic energy term (along with the other terms) when you set up your conservation of energy problem).

Answer 1

Angular velocity, w, can be determined as Delta U = I w^2/2 here Delta U is change in potential energy Delta U = (-p_i middot E vector) - (p vector_f middot E vector) p_i rightarrow initial dipole moment p_f rightarrow final dipole moment I rightarrow moment of inertia Here moment of inertia will be, I = 2 m_s l^2/4 + m_r ln^2/12 m_s rightarrow mass of sphere, m_r rightarrow mass of rod l rightarrow length of rod I = 2 times 0.001 times (0.15)^2/4 + 0.004 times (0.15)^2/12 I = 1.875 times 10^-5 kg m^2 Now, Delta U = -ql E cos 90 degree + q l E cos 0 degree Delta U = qlE q rightarrow charge of sphere solving, w = squareroot 2qlE/I = squareroot 2 times 3 times 10^-9 times 0.15 times 1000/1.875 times 10^-5 w = 0.219 rad/s