A point charge causes an electric flux of `-1.0xx10^(3) N m^(2)//C` to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface ? (b) What is the is the value of the point charge ?

Explanation

(a) Electric flux, `phi=-1.0xx10^(3)Nm^(2)//C`
Radius of the Gaussian surface,
r= 10.0 cm
Electric flux piercing out through a surface depends on the net charge enclosed inside a body. It does not depend on the size of the body. If the radius of the Gaussian surface is doubled, then the flux passing through the surface remains the same i.e.,
`-10^(3)Nm^(2)//C`.
(b) Electric flux is given by the relation,
`phi=(q)/(in_(0))`
Where,
q = Net charge enclosed by the spherical surface
`in_(0)` = Permittivity of free space = `8.854xx10^(-12)N^(-1)C^(2)m^(-2)`
`thereforeq=phiin_(0)`
`=-1.0xx10^(3)xx8.854xx10^(-12)`
`=-8.854xx10^(9)C`
`=-8.854nC` ltBrgt Therefore, the value of the point charge is −8.854 nC.