Two charged particles each of mass 9.8 ~g and charges +20 C and -20 C are attached to the two ends of a massless and rigid uniform non-conducting rod of length 50 ~cm . This arrangement is held in a uniform electric field of 12.1 NC ⁻¹ , such that the rod makes a very small angle with the field direction. If the rod is set free, the minimum time needed for the rod to become parallel to the direction of the electric f

Step-by-step solution

This arrangement of electric dipole in electric field will undergo SHM, when the rod is set free. Time period of this SHM is given by T=2 I PE where, I= moment of inertia of dipole, p= electric dipole moment and E= electric field. I=2 m r^2 aligned & mass, m=9.8 10⁻³ ~kg , r= 50 2 10⁻² & I=2 9.8 10⁻³ ( 50 2 10⁻² )^2 & I=1225 10⁻⁴ k -g^2 m⁻²=10⁻⁵ C - m & p=q(2 l)=20 10⁻⁶ 50 10⁻² & E=121 ~N / C & T=2 1225 10⁻⁴ 10⁻⁵ 121 =2 3.14 3.181 & T=19.98 20 ~s aligned But time taken by the rod to become parallel will be T / 4 ,