Consider a metallic sphere of radius 1m and having a bulk modulus of `(1/(4pi^(2)))xx10^(11)N//m^(2)`. Now if a negative charge of `20xx10^(3)muC` is given to the sphere, then the voume strain in the sphere is `X xx 10^(-5)`. What is X=?

Answer

`05.65`

Explanation

Bulk modulus `K=("volume stress")/("volume strain")`
Electrostatic pressure `P=(sigma^(2))/(2epsilon_(0)k)`
`:.` volume strain `=(sigma^(2))/(2k epsilon_(0))xx1/K`
`=(Q/(4pi R^(2)))^(2)xx1/(2 k epsilon_(0))xx1/K`
……….`( :. sigma =Q/A)`
`=(Q^(2))/(16pi^(2)xxR^(4)xx2xxepsilon_(0)xx1/(4pi^(2))xx10^(11))`
.......(For air k=1)
`=((20xx10^(-3))^(2))/(8xx1^(4)xx8.85xx10^(-12)xx10^(11))`
`=(400xx10^(-6))/(8xx8.85xx10^(-1))`
`=50/8.85xx10^(-5)`
`=5.649xx10^(-5)`
`:.` Volume strain `=5.65xx10^(-5)`
......(Rebounding off to 2 decimal places)