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
A. `30 cm`
B. `6 m`
C. `5cm`
D. `3 m`

Answer 1

Correct Answer - D
Given: `(b - a) = 1 xx 10^(-3) m` ..(i)
and `C = 4pi epsilon_(0) ((ab)/(b - a)) = 1 xx 10^(-6)`
`rArr 1 xx 10^(-6) = (1)/(9 xx 10^(9)) ((ab)/(10^(-3)))`
`rArr ab = 9` ..(ii)
From equations (i) and (ii)
`b - (9)/(b) = (1)/(1000) rArr 1000 b^(2) - b - 9000 = 0`
`rArr b = (1+-sqrt((-1)^(2) -4(1000) (-9000)))/(2 xx 1000)`
{Solving of quadratic equation }
`rArr b = (1+-sqrt(36 xx 10^(6)))/(2000) ~~sqrt(36 xx 10^(6))/(2000) = 3m`