A parallel plate capacitor with width 4 cm , length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V . A dielectric slab of dielectric constant 5 having length 1 cm , w

Question

A parallel plate capacitor with width 4 cm , length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V . A dielectric slab of dielectric constant 5 having length 1 cm , width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _____ ϵ 0 J . (Where ϵ 0 is the permittivity of free space)

TestHub · Accepted Answer

The figure below shows the parallel plate capacitor with dielectric slab placed in between the plates.
Now, the effective capacitance of the combination is
$C_{eff} = [\frac{ε_{0} (7 \times 4)}{\frac{4}{10}} + \frac{5 ε_{0} (1 \times 4)}{\frac{4}{10}}] \times 10^{- 2}$
$= [70 ε_{0} + 50 ε_{0}] \times 10^{- 2} = 120 ε_{0} \times 10^{- 2}$
$\Rightarrow C_{eff} = 1.2 ε_{0}$
Electrostatics energy of this system is $= \frac{1}{2} C_{eff} V^{2}$
$= \frac{1}{2} (1.2) ε_{0} (20) (20) = 240 ε_{0}$

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