A heavy block is attached to the ceiling by a spring that has a force constant ' 
'. A conducting rod is attached to block. The combined mass of the block and the rod is m. The rod can slide without friction along two vertical parallel rails, which are a distance 
apart. A capacitor of known capacitance 
is attached to the rails by the wires. The entire system is placed in a uniform magnetic field B. Find the time period T of the vertical oscillations of the block. Neglect the electrical resistance of the rod and all wires-
Text Solution
Verified by ExpertsA
Using Kirchoff ’s equation
– Blv = 0 [Where 
]
q = CBlv
i = 
= CBl 
Magnetic force on AB bar or block = Bil
F mag = B 2 l 2 C 
For initial equilibrium,
kx = mg ... (1)
mg – k(x + y) – B 2 l 2 C 
= ma ... (2)
mg – kx – ky – B 2 l 2 Ca = ma
a = 
Comparing equation of a by a = – ω 2 y
ω = 
T = 
= 
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