The capacitance of a spherical condenser is $1 \mu \mathrm{F}$ . If the spacing between the two spheres is 1 mm, then the radius of the outer sphere is
Text Solution
Verified by ExpertsD
Given: (b – a) = 1 × × 10 –3 m ..... (i)
and $c = 4 \pi \varepsilon_0 \left(\frac{ab}{b - a}\right) = 1 \times 10^{-6}$
⇒ ⇒ $1 \times 10^{-6} = \frac{1}{9 \times 10^{9}} \left(\frac{ab}{10^{-3}}\right)$
⇒ ⇒ ab = 9 ..... (ii)
From equations (i) and (ii)
$b - \frac{9}{b} = \frac{1}{1000}$ ⇒ ⇒ 1000 b 2 – b – 9000 = 0
⇒ ⇒ $b = \frac{1 \pm \sqrt{(-1)^2 - 4(1000)(-9000)}}{2 \times 1000}$
{Solving of quadratic equation}
⇒ ⇒ $b = \frac{1 \pm \sqrt{36 \times 10^{6}}}{2000} \approx \frac{\sqrt{36 \times 10^{6}}}{2000} = 3m.$
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems