Two long conducting rods suspended by means of two insulating threads as shown in Fig. are connected to a charged capacitor through a switch which is initially open. At the other end, they are connected by a loose wire.
The capacitor has a charge Q and mass per unit length of the rod is λ . The effective resistance of the circuit after closing the switch is R.
Find the velocity of each rod when the capacitor is discharged after closing the switch. Assume that the displacement of rods during the discharging time is negligible.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. The impulsive force due to (antiparallel) discharging currents is equal to the change in momentum or
λ v = 
dt = 
where i = discharging current
Now q = Qe –t/RC ⇒ | i | = 
Magnetic force per unit length between two current carrying wires is
= 
= 
Impulse due to this force = 
dt.
Hence λ v = 
= 
or v = 
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