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In a Van-De Graaff type generator a sphe...

In a Van-De Graaff type generator a spherical metal shell is to be a `15 xx 10^(6)` V electrode. The dielectric strength of the gas surrounding the electrode is `5xx10^(7) Vm^(-1)`. What is the minimum radius of the spherical shell required ?

Text Solution

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Maximum acceptable potential
`V=1.5xx10^(6)` V
For safety E = 10 % of dielectric strength
`= 5 xx10^(7)`
`= 5xx10^(7)xx(10)/(100)`
`= 5xx10^(6) Vm^(-1)`
Potential for spherial shell
`V = (kq)/(r)`
and electric field `E = (kq)/(r^(2))`
`:. (V)/(E) =r `
`:.` Required minimum radius
`r = (V)/(E) = (1.5xx10^(6))/(5xx10^(6))`
`:. r = 3xx10^(-1) `m = 30 cm
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