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)


1