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A conducting rod of mass m and length l is suspended horizontally with springs each of force constant K in the presence of uniform magnetic field B₀ as shown. A completely charged capacitor having charge $Q_{0} = C ε$ is connected to rod as shown when rod is in equilibrium.

Neglect any resistance, any inductance in the circuit. Consider connecting wires are extremely flexible and having negligible mass. Connecting wire does not exert any force on the rod.
Choose correct statement(s):

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Maximum speed of rod is $\frac{B l C ε}{m}$

Time period of Oscillation is $2 π \sqrt{\frac{m}{2 K}}$

Amplitude of Oscillation is $\frac{B l C ε}{\sqrt{2 m K}}$

None of these

answer is A, B, C.

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Detailed Solution

(i) Capacitor discharge in zero time inertial

$\int (B I l) d t = m \int d v B l Q = m v \frac{B l C ε}{m} = v$

$i i) T = 2 π \sqrt{\frac{m}{2 K}} i i i) A \sqrt{\frac{2 K}{m}} = \frac{B l C ε}{m} A = \frac{B l C ε}{\sqrt{2 m K}}$

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