The radii of the inner and outer spheres of a condenser are $9\,cm$ and $10\,cm$ respectively. If the dielectric constant of the medium between the two spheres is $6$ and charge on the inner sphere is $18 \times {10^{ - 9}}\;coulomb$, then the potential of inner sphere will be, if the outer sphere is earthed........$volts$
Medium
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(b) Given system is a spherical capacitor
So capacitance of system $C = K \times 4\pi {\varepsilon _0}\left[ {\frac{{{r_1}{r_2}}}{{{r_2} - {r_1}}}} \right]$
$ = \frac{6}{{9 \times {{10}^9}}}\left[ {\frac{{9 \times 10}}{1}} \right] \times {10^{ - 2}} = 6 \times {10^{ - 10}}\,Farad$
Now potential of inner sphere will be equal to potential difference of the capacitor. So $V = \frac{q}{C} = \frac{{18 \times {{10}^{ - 9}}}}{{6 \times {{10}^{ - 10}}}} = 30\,V$
So capacitance of system $C = K \times 4\pi {\varepsilon _0}\left[ {\frac{{{r_1}{r_2}}}{{{r_2} - {r_1}}}} \right]$
$ = \frac{6}{{9 \times {{10}^9}}}\left[ {\frac{{9 \times 10}}{1}} \right] \times {10^{ - 2}} = 6 \times {10^{ - 10}}\,Farad$
Now potential of inner sphere will be equal to potential difference of the capacitor. So $V = \frac{q}{C} = \frac{{18 \times {{10}^{ - 9}}}}{{6 \times {{10}^{ - 10}}}} = 30\,V$
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