Question

A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 10³ N/C and points radially inward, what is the net charge on the sphere?

Answer 1

Electric field intensity (E) at a distance (d) from the centre of a sphere containing net charge q is given by the relation,

`E = 1/(4piε_0 d^2)`

Where,

E = Electric field = 1.5 × 10³ N/C

d = Distance from the centre = 20 cm = 0.2 m

ε₀ = Permittivity of free space

`1/(4piε_0)` = 9 × 10⁹ N m² C⁻²

∴ `E = 1/(4piε_0) * q/d^2`

`q = (E d^2)/(1/(4piε_0))`

= `(1.5 xx 10^3 xx (0.2)^2)/(9 xx 10^9)`

= `(1.5 xx 10^3 xx 0.04)/(9 xx 10^9)`

= 0.00667 × 10⁻⁶ C

= 6.67 × 10⁻⁹ C 

Since the electric field points radially inward, the charge is negative.

q = − 6.67 nC