Question

The capacity of a spherical condenser is $1\mu F$. If the spacing between the two spheres is $1mm$, the radius of the outer sphere is.

• A. $3cm$
• B. $6cm$
• C. $3m$
• D. $6m$

Answer 1

The correct option is C $3m$

Capacity of spherical capacitor bounded by two spheres is given by:

$C=\frac{4\pi {ϵ}_0{R}_1{R}_2}{R_2-R_1}$------------(i)

Now, according to question:

$C=1\mu F={10}^{-6}F$

and $R_2-R_1=1mm={10}^{-3}m$

So, by putting the value in eq. (i), we get:

${10}^6=\frac{4\pi {ϵ}_0{R}_1{R}_2}{{10}^{-3}m}$

$⟹R_1{R}_2=\frac{1}{4\pi {ϵ}_0}\times {10}^{-6}\times {10}^{-3}$

As we know, $R_1\approx R_2$ and $\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$

So, $R_2^2=9\times {10}^9\times {10}^{-9}$

$⟹R_2=\sqrt{9}=3m$