First slide

Capacitance

Question

The capacitance of a spherical condenser is 1 $μ$ F, If the spacing between the two spheres is 1 mm, the radius of the outer sphere is

Difficult

A

30 cm
B

3 cm
C

6 cm
D

3 m

Solution

$C = 4 {πε}_{0} (\frac{ab}{b - a})$
Given $C = 1 μF = 1 \times 10^{- 6} F$
and $(b - a) = 1 \times 10^{- 3} m$
$\begin{array}{ll} ∴ 1 \times 10^{- 6} = \frac{1}{9 \times 10^{9}} \times \frac{(b - 1 \times 10^{- 3}) (b)}{1 \times 10^{- 3}} \\ 9 = b^{2} - b \times 10^{- 3} \approx b^{2} \\ ∴ b = 3 metre \end{array}$

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