As shown in figure, the two parallel conducting rails, in a horizontal plane, are connected at one end by an inductor of inductance L . A slider (metallic) of mass m , is imparted a velocity v 0 , upon the rails, as shown in figure. The period of oscillation of the conducting rod is

Step-by-step solution

From energy conservation (there are no dissipative forces)- E = 1 2 m v 2 + 1 2 L I 2 ⇒ m 2 × 2 v d v d t + L 2 × 2 I d I d t = 0 m v d v d t = - I L d I d t The emf induced in an inductor is E = L d I d t = B l v ⇒ L d I d t = B l d x d t ⇒ L d I = B l d x ⇒ I = B l L x The force acting on a current-carrying conductor is m d v d t = - I B l ⇒ d v d t = - I B l m Substituting the value of I we get d v d t = - B l L x B l m ⇒ a = - B 2 l 2 m L x We got acceleration in th