A conducting sphere fo radius 10 cm has an unknown charge. If the electric field 20 cm from the center of the sphere is `1.5xx10^(3) N//C` and points radially inwards, what is the net charge on the sphere ?

Explanation

Electric field intensity (E) at a distance (d) from the centre of a sphere containing net charge q is given by the relation,
`E=(q)/(4piin_(0)d^(2))`
where, ltBrgt q = Net charge = `1.5xx10^(3)N//C`
d = Distance from the centre = 20 cm = 0.2 m
`in_(0)` = Permittivity of free space
And, `(1)/(4piin_(0))=9xx10^(9)Nm^(2)C^(-2)`
`thereforeq=E(4piin_(0))d^(2)`
`=(1.5xx10^(3)xx(0.2)^(2))/(9xx10^(9))`
`=6.67xx10^(9) C`
`=6.67nC` ltBrgt Therefore, the net charge on the sphere is 6.67 nC.