A point charge causes an electric flux of −1.0 × 10^{3} Nm^{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 value of the point charge?

#### Solution

**(a) **Electric flux, Φ = −1.0 × 10^{3} N m^{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} N m^{2}/C.

**(b) **Electric flux is given by the relation,

`phi = "q"/in_0`

Where,

q = Net charge enclosed by the spherical surface

∈_{0} = Permittivity of free space = 8.854 × 10^{−12 }N^{−1 }C^{2 }m^{−2}

∴ `"q" = phiin_0`

= −1.0 × 10^{3} × 8.854 × 10^{−12}

= −8.854 × 10^{−9} C

= −8.854 nC

Therefore, the value of the point charge is −8.854 nC.