Two charged spherical conductors of radii R_{1} and R_{2} when connected by a conducting wire acquire charges q_{1} and q_{2} respectively. Find the ratio of their surface charge densities in terms of their radii.

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#### Solution

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

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

For spherical conductor *R _{1}*, the surface charge density is given by:

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

Similarly, for spherical conductor *R _{2}*, 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:

q_{1}=q_{2}

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

Concept: Conductors and Insulators Related to Electric Field

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