Question

Two tiny spheres, each of mass $M$, and charges $+q$ and $-q$ respectively, are connected by a massless rod of length, $L$. They are placed in a uniform electric field an an angle $\theta$ with the $\overrightarrow{E}(\theta =0^o)$. Calculate the minimum time in which the dipole axis becomes parallel to the field line.

Answer 1

$⟹\tau =pE\sin \theta ,($as $\theta \to 0,\sin \theta \to \theta )$
$⟹\tau =-\left(pE\right)\theta$ (If we assume angular displacement to be anti-clockwise, torque is clockwise)
$⟹\alpha =-\left(\frac{pE}{l}\right)\theta =-{\omega }^2\theta$
As torque is proportional to '$\theta$' and oppositely directed, the motion will be a angular S.H.M.
Here, $p=q.L.$ and moment of inertia, $l=M$
$(L/2{)}^2+M(L/2{)}^2=M{L}^2/2$
The minimum time required to align itself is $T/4$sec.