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Define surface density of charge and po...

Define surface density of charge and potential of a charged and potential of a charged spherical conductor. Establish a relation between them.

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Surface density of charge is defined as the charge per unit area of a charged conductor . If r is the radius of a spherical conductor having charge q, then its surface density of charge,
`sigma = (q)/(4pi r^(2))` …(i)
Electric potentail of the spherical charged condutor,
`V = (q)/(4pi in_(0) r) or q = 4pi in_(0) r xx V`
Putting this value in (i), we get
`sigma = (4pi in_(0) rV)/(4pi r^(2)) = (in_(0) V)/(r )`
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