Question

Rectangular plates of a parallel plate capacitor have dimensions l & b. A dielectric of constant 3 is inserted between the plates while battery of constant voltage V remains connected between the plates (see figure). Magnitude of net electrostatic force experienced by dielectric due to capacitor is :

• A. $\frac{l{V}^2{ϵ}_0}{d}$
• B. $\frac{l{V}^2{ϵ}_0}{2d}$
• C. $\frac{b{V}^2{ϵ}_0}{2d}$
• D. $\frac{b{V}^2{ϵ}_0}{d}$

Answer 1

Answer: (D)

$\frac{b{V}^2{ϵ}_0}{d}$

$U=\frac{1}{2}C{V}^2$

$F=-\frac{dU}{dx}=\frac{-V^2}{2}\frac{dC}{dx}$

$C=\frac{b(l-x){ϵ}_0}{d}+\frac{kbx{ϵ}_0}{d}$

$\Rightarrow F=\frac{-V^2}{2}(k-1)\frac{b{ϵ}_0}{d}$

$\because k=3,$

$F=\frac{b{V}^2{ϵ}_0}{d}$