Question

If a slab of insulating material (conceptual). $4\times 10^{-3}m$ thick is introduced between the plates of a parallel plate capacitor, the separation between the plates has to be increased by $3.5\times 10^{-3}m$ to restore the capacity to original value. The dielectric constant of the material will be

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

Answer: (B)

If $k$ be the dielectric constant, the distance increased due to introduced dielectric is $x=t-\frac{t}{k}\Rightarrow x=t\left(1-\frac{1}{k}\right)$
Where, $t\to$ thickness of the dielectric.
According to the question,
$x=3.5\times 10^{-3}m$
$t\left(1-\frac{1}{k}\right)=3.5\times 10^{-3}$
$1-\frac{1}{k}=\frac{3.5\times 10}{4\times 10}=\frac{3.5}{4}$
$\frac{1}{k}=1-\frac{35}{4}=\frac{0.5}{4}=0.125$
$k=8$