A wire of mass m and length ℓ can slide freely on a pair of smooth, vertical rails figure. A magnetic field B exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance C. Find the acceleration of the wire neglecting any electric resistance.
Given:
Mass = m
Length = l
Magnetic field = B
Capacitance = C
Formula used:
Induced emf 
… (i), where B = magnetic field, l = length, v = velocity
Also, we know that 
… (ii), where q = charge, C = capacitance.
Hence, 
⇒ 
.. (ii)
Therefore, current 
, where q = charge, t = time
=> 
… (iii), where a = acceleration
Therefore, net force on rod = weight - magnetic force = mg - ilB .. (iv), where m = mass, g = acceleration due to gravity, i = current, l = length, B = magnetic force
From newton’s second law of motion, F = ma … (v), where f= force, m = mass, a = acceleration
Therefore, 
(from (iii))
⇒ 
=>acceleration 
(Ans)