A uniformly charged spherical conductor of radius 10 cm has a total charge of 4 10⁻⁶ C . The magnitude of the electric field produced by this charge distribution at a certain point outside the sphere is 9 10⁵ N C ⁻¹ . What is the distance of this point from the centre of the sphere? ( 1 4 ₀ = 9 10^9 N m ^2 C ⁻² )

Step-by-step solution

The electric field outside a uniformly charged spherical conductor at a distance r from its centre is given by: E = 1 4 ₀ Q r^2 Rearranging for r^2 : r^2 = 1 4 ₀ Q E Substituting the given values: r^2 = 9 10^9 4 10⁻⁶ 9 10^5 r^2 = 36 10^3 9 10^5 = 4 10⁻² m ^2 Taking the square root: r = 0.2 m = 20 cm Answer: 20 cm