In the figure, a conducting rod of length l = 1 meter and mass m = 1 kg moves with an initial velocity, u = 5 m s - 1 . On a fixed horizontal frame containing inductor L = 2 H and resistance R = 1 Ω . PQ and MN are smooth, conducting wires. There is a uniform magnetic field of strength B = 1 T . Initially, there is no current in the inductor. Find the total charge in coulomb, flown through the inductor by the time ve

Step-by-step solution

Let i 1 and i 2 be the current through L and R at any time t ∴           i = i 1 + i 2   ⇒     B l v R = i 2 and B l v = L d i 1 d t Force on conducting rod = m d v d t = - i l B = - i 1 + B l v R l B ⇒         m d v =   - l B   i 1 d t - B 2 l 2 R v   d t   ⇒         m ∫ d v = - l B   ∫ i 1 d t - B 2 l 2 R   ∫ v   d t ⇒         m v f