Question

Two charged spherical conductors of radii R₁ and R₂ when connected by a conducting wire acquire charges q₁ and q₂ respectively. Find the ratio of their surface charge densities in terms of their radii.

Answer 1

 

 

The surface charge density for a spherical conductor is given by:

`sigma=Q/(4pir^2)`

For spherical conductor R₁, the surface charge density is given by:

`sigma_1=q_1/4piR_(1^2)`

Similarly, for spherical conductor R₂, the surface charge density is given by:

`sigma_2=q_2/(4piR_(2^2))`

`:.sigma_1/sigma_2=(q_1/q_2)((R_(2^2))/R_(1^2))`

Since the two conductors are connected, we have:

q₁=q₂

`:.sigma_1/sigma_2=R_(2^2)/R_(1^2)`