A conducting rod of mass M and length L can oscillate like a pendulum in a vertical plane about point O. The lower end of the rod glides smoothly on a circular conducting arc of radius L. The circular arc is connected to point O of the rod through a capacitor of capacitance C. The entire device is kept in a uniform horizontal magnetic field B directed into the plane of the Figure. Disregard resistance of any component. The rod is deflected through a small angle `theta_(0)` from vertical position and released at time t = 0. (a) Write the deflection angle `(theta)` of the rod as a function of time t. (b) If the capacitor is replaced with a resistor what kind of motion do you expect? Give qualitative description only.

A conducting rod of mass M and length L can oscillate like a pendulum

1.	A conducting rod of mass M and length L can oscillate like a pendulum in a vertical plane about point O. The lower end of the rod glides smoothly on a circular conducting arc of radius L. The circular arc is connected to point O of the rod through a capacitor of capacitance C. The entire device is kept in a uniform horizontal magnetic field B directed into the plane of the Figure. Disregard resistance of any component. The rod is deflected through a small angle `theta_(0)` from vertical position and released at time t = 0. (a) Write the deflection angle `(theta)` of the rod as a function of time t. (b) If the capacitor is replaced with a resistor what kind of motion do you expect? Give qualitative description only.
Answer» Correct Answer - (a) `theta = theta_(0) cos omega t` where `omega = [(6Mg)/(4ML + 3B^(2)L^(3)C)]^(1//2)` (b) Oscillations die after some time.

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