11Is the time period is
T = 8 [ (l-x) mld / e0 AV2 (K-1)] 1/2
the plare area is A.....dielectric constant is K
released from rest wid a l;ength a inside the capacitor nad length of the capacitor is L
neglect air friction or gravbity.....fiund the motiion n if SHM find its time period
[please note in the diagram there is aslight error.....lenrgth of the dielectric initially inside the capacitor is a and lenghth of the dielectric is L]
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11 Answers
1it will not be SHM
if we remove battery then it is an SHM
this is a periodic of motion of period which I am not in a mood to post
lol
62http://www.targetiit.com/iit-jee-forum/posts/4th-december-2008-808.html
This is similar.. read this oen.. i think what rohan had done is corrct..
1arre yaar bahut bada hai
use F=-dU/dx
find U at any time instant as a function of x
capacitors are in paralle
us C=C1+C2
then find U=1/2CV2
and then dU/dx
once u find force apply some equations of motion
and u r done
11
Since the force on a dielectric at const potential V is given by
F = e0 b V 2 (K-1) / 2d [electric forces pulls the slab inward with a const force]
where b = width of plate = A / l
Thus acc of slab , a = F/m
a = e0 (A/l ) V 2 (K-1) / 2md
The =lbm posn of the slab is at the instant when the slab is fully inside the paltes. So, the slab will execute oscillations in the phases.
Let the time taken by the slab to reach completely inside the paltes = t (say) = T/4 [WHERE T is the tme period]
Using s= (1/2)at2 where s = l-a then t = √s/a = [4 (l-a)mdl / e0AV2 (K-1)] 1/2
therefore, T = 4 t =ans