In Fig., the capacitors have plate area A = l × b, separation 'd'.
If the slab is displaced slightly, find the time period of the oscillation. Is it simple harmonic? Given mass of the dielectric = m.
Text Solution
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Sol. When the slab is displaced by a distance x, the work done is = change in stored energy + work done by battery
Initial capacitance of the capacitors,
C = 
+ 
Final capacitances
C 1f = 
+ 
C 2f = 
+ 
Change in energy stored = – 
E 2 [C 1f – C] + 
E 2 [C 2f – C]
Work done by battery = E dq
= E × E[(C 1f – C) – (C 2f – C)]
Work done = 
× (k – 1)
Expression for force can be obtained by differentiating expression for W. For a conservative force, – 
= F
Hence F = 
Net acceleration a = 
= 
(k – 1)E 2 Motion is oscillatory but not SHM because acceleration is constant. For constant acceleration motion,
t = 
Time period = 4t = 
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