Question

A large parallel plate capacitor is made of two metal plates of size $2m\times 1m$. It has a dielectric slab made of two dielectrics of permeability $K_1$ and $K_2$ as shown in the figure, the distance between them being 0.1m. It is charged by a battery of 1000V after which the battery is disconnected. Now the dielectric slab is puled out by 10cm. The work done in doing so is (ignore the gap between the plates and the dielectric slab)

• A. $2.5\times {10}^5{ϵ}_{0}J$
• B. $-2.5\times {10}^5{ϵ}_{0}J$
• C. $5\times {10}^5{ϵ}_{0}J$
• D. $-5\times {10}^5{ϵ}_{0}J$

Answer 1

The correct option is D $-5\times {10}^5{ϵ}_{0}J$

$\Delta C=\frac{(K_1-K_2){ϵ}_0{A}^{\prime }}{d}=\frac{(3-2){ϵ}_0\times 0.1\times 1}{0.1}{ϵ}_0{U}_{initial}=\frac{Q^2}{2C}{U}_{final}=\frac{Q^2}{2(C+\Delta C)}\therefore W=U_{final}-U_{initial}=\frac{1}{2}\Delta C{V}^2=-5\times {10}^5{ϵ}_{0}J$