Sucking up a dielectric Part A A parallel plate capacitor has plates of dimensio

Question

Sucking up a dielectric Part A A parallel plate capacitor has plates of dimension L × L that are separated by a distance d L . The capacitor is charged up to a charge Q , disconnected from any source of voltage, and then an edge of the the capacitor is placed in a liquid with dielectric constant K and mass density p. The gravitational force i:s acting downward in the figure. Find the equilibrium height of the liquid. Assume the equilibrium height is much smaller than L so you do not have to solve a cubic equation. Hint: Remember that force is F =-VU and balance the forces on the liquid. Alternatively, you can think ofit as finding the minimum in potential energy Hint: Remember that force is -VU and balance the forces on the liquid. Alternatively, you can think of it as finding the minimum in potential energy

Explanation / Answer

As we know that,

Parallel plate capacitor is placed inside the liquid having dielectric constant K.

But we don’t know how much height of capacitor is inside the liquid?

We have to calculate this height.

So, we can start with basic assumption, suppose this height is equal to thickness of dielectrics

i.e h= t

So we use the formula,

C = A /(d-t+(t/K))

Put t = h

C = A /(d-h+(h/K))

(d-h+(h/K)) = A /C

d-h((K-1)/K) = A /C

Therefore,

h((K-1)/K) = (A /C)-d

h = (A-Cd /C)*(K/K-1)

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