In the arrangements shown in Fig. there is a uniform magnetic filed B 0 normal to the plane of paper. The connector is smooth and conducting and is has a mass m and length l.
The connector is pushed against the spring so that the spring has compression x 0 . The connector is released at t = 0. Find the time it will take to come to its original position again. The spring is non-conducting. The resistance of the rails is zero and neglect its self-inductance.
Text Solution
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Sol. Let us say at any time t the rod is at a distance x from its original position
v = 
e (induced emf) = Blv = bl 
Charge on the capacitor q = Ce = BlC 
Current i = 
= BlC 
Force on the conductor due to this current,
F = ilB = B 2 l 2 C 
Net force on the connector to the right,
m 
⇒ 
The acceleration is proportional to x and opposite to it and hence we can say the motion will be SHM.
With T = 2 π 
and the time taken will be 
.
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