Electrostatics Question 68
Question: The diameter of each plate of an air capacitor is $ 4cm $ . To make the capacity of this plate capacitor equal to that of $ 20cm $ diameter sphere, the distance between the plates will be [MP PET 1996]
Options:
A) $ 4\times {{10}^{-3}}m $
B) $ 1\times {{10}^{-3}}m $
C) $ 1cm $
D) $ 1\times {{10}^{-3}}cm $
Show Answer
Answer:
Correct Answer: B
Solution:
Capacity of spherical conductor of 20 cm diameter $ C _{1}=4\pi {\varepsilon _{0}}r=4\pi {\varepsilon _{0}}\times 10 $
Capacity of parallel plate air capacitor $ C _{2}=\frac{{\varepsilon _{0}}A}{d}=\frac{{\varepsilon _{0}}[\pi {{(2)}^{2}}]}{d}=\frac{{\varepsilon _{0}}\times 4\pi }{d} $ Hence $ C _{1}=C _{2} $
therefore $ 40\pi {\varepsilon _{0}}=\frac{4\pi {\varepsilon _{0}}}{d} $
therefore $ d={{10}^{-3}}m $
