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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.
Solution
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)`
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