By reference to electric field lines, explain why, for points outside an isolated spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre.

Question 23

(a) By reference to electric field lines, explain why, for points outside an isolated spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre. [2]

(b) Two isolated protons are separated in a vacuum by a distance x.

(i) Calculate the ratio

  electric force between the two protons    .

gravitational force between the two protons

 [3]

(ii) By reference to your answer in (i), suggest why gravitational forces are not considered when calculating the force between charged particles. [1]

[Total: 6]

Reference: Past Exam Paper – June 2016 Paper 42 Q6

Solution:

(a) The electric field lines are radial (and perpendicular to the surface of the sphere) and appear to come from the centre.

(b)

(i)

{Electric force = Q₁Q₂ / 4πε0x²  

The charge of a proton is + 1.6 × 10^-19 C}

FE = (1.6 × 10^-19)² / 4πε0x²

{Gravitational force = GMm / x²

As given in the list of data, mass of proton = 1.67 × 10^-27 kg}

FG = G × (1.67 × 10^-27)² / x²

FE / FG = (1.6 × 10^-19)² × (8.99 × 10⁹) / [(1.67×10^-27)² × (6.67×10^-11)]

FE / FG = 1.2 (1.24) × 10³⁶    

(ii)

{ FE / FG = 1.2 × 10³⁶  

FE = 1.2 × 10³⁶ ×FG

The electric force is much greater than the gravitational force.}

FE ≫ FG