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Constructing Parallel Plate Capacitor using Paper Sheets

Try this problem, useful for Physics Olympiad based on Constructing Parallel Plate Capacitor.

The Problem: Constructing Parallel Plate Capacitor

Suppose you are to construct a parallel plate capacitor of (1\mu F) by using paper sheets of thickness (0.05mm) as dielectric and a number of circular parallel metal foils connected alternately. If the dielectric constant of paper is (4) and radius of each foil is (10cm) then find the number of metal foils needed for this purpose.

Solution:

If there are (n) foils connected alternately then it can be considered as the parallel combination of (n-1) capacitors. Thus capacitance,
$$C=(n-1)\frac{\epsilon A}{d}$$
Putting $$C=1\mu F=10^{-6}\mu F$$
$$\epsilon=K\epsilon_0=48.85410^{-12}F/m$$
$$A=\pi r^2=\pi(0.1)^2m^2$$
and $$d=0.05*10^{-3}$$ in the formula $$C=(n-1)\frac{\epsilon A}{d}$$  we get (n=46)
Hence (46) metal foils are required.