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)

Step-by-step solution

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 = ε 0 7 × 4 4 10 + 5 ε 0 1 × 4 4 10 × 10 - 2 = 70 ε 0 + 50 ε 0 × 10 - 2 = 120 ε 0 × 10 - 2 ⇒ C eff   = 1 . 2 ε 0 Electrostatics energy of this system is = 1 2 C eff V 2 = 1 2 1 . 2 ε 0 20 20 = 240 ε 0