The diameter of each plate of an air capacitor is $4\,cm$. To make the capacity of this plate capacitor equal to that of $20\,cm$ diameter sphere, the distance between the plates will be
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(b) Capacity of spherical conductor of $20\, cm$ diameter ${C_1} = 4\pi {\varepsilon _0}r = 4\pi {\varepsilon _0} \times 10$
Capacity of parallel plate air capacitor
${C_2} = \frac{{{\varepsilon _0}A}}{d} = \frac{{{\varepsilon _0}[\pi {{(2)}^2}]}}{d} = \frac{{{\varepsilon _0} \times 4\pi }}{d}$
Hence ${C_1} = {C_2}$ $==>$ $40\pi {\varepsilon _0} = \frac{{4\pi {\varepsilon _0}}}{d}$ $==>$ $d = {10^{ - 3}}\,m$
Capacity of parallel plate air capacitor
${C_2} = \frac{{{\varepsilon _0}A}}{d} = \frac{{{\varepsilon _0}[\pi {{(2)}^2}]}}{d} = \frac{{{\varepsilon _0} \times 4\pi }}{d}$
Hence ${C_1} = {C_2}$ $==>$ $40\pi {\varepsilon _0} = \frac{{4\pi {\varepsilon _0}}}{d}$ $==>$ $d = {10^{ - 3}}\,m$
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