Electrostatics Question 20
Question: The capacitance of a spherical condenser is $ 1\mu F $ . If the spacing between the two spheres is$ 1mm $ , then the radius of the outer sphere is [CPMT 1989]
Options:
A) $ 30cm $
B) $ 6m $
C) $ 5cm $
D) $ 3m $
Show Answer
Answer:
Correct Answer: D
Solution:
Given : (b ? a) = $1 x {10}^{-3}$ m ….. (i) and $ C=4\pi {\varepsilon _{0}}( \frac{ab}{b-a} )=1\times {{10}^{-6}} $
therefore $ 1\times {{10}^{-6}}=\frac{1}{9\times 10^{9}}( \frac{ab}{{{10}^{-3}}} ) $
therefore $ ab=9 $ ….. (ii)
From equations (i) and (ii) $ b-\frac{9}{b}=\frac{1}{1000} $
therefore 1000 b2 - b - 9000 = 0
therefore $ b=\frac{1\pm \sqrt{{{(-1)}^{2}}-4(1000)(-9000)}}{2\times 1000} $ {Solving of quadratic equation}
therefore $ b=\frac{1\pm \sqrt{36\times 10^{6}}}{2000}\approx \frac{\sqrt{36\times 10^{6}}}{2000}=3m. $
