Question

The area of each plate of a parallel plate capacitor is $100c{m}^2$ and the distance between the plates is $1mm$. It is filled with mica of dielectric $6$. The radius of the equivalent capacity of the sphere will be

• A. $47.7m$
• B. $4.77m$
• C. $477m$
• D. None of the above

Answer 1

The correct option is B $4.77m$

Capacitance of parallel plate capacitor fillerd with dielectric is
$C=\frac{{\epsilon }_{0}AK}{d}$
Capacitance of a spherical conductor
$C=4\pi {\epsilon }_{0}r$
For equal capacitance of parallel plate and sphere
$C=\frac{{\epsilon }_{0}AK}{d}=4\pi {\epsilon }_{0}r$
Here $r$ is radius of sphere of equivalent capacity
$\Rightarrow r=\frac{AK}{4\pi d}=\frac{100\times {10}^{-4}\times 6}{1\times {10}^{-3}\times 4\times 3.14}=\frac{15}{3.14}=4.77m$