1.

Consider A, D and C to be the co-centric shells of metal . Their radii are a ,b and c respectively (a < b < c). Their surface charge densities are sigma, -sigma and sigma respectively. Calculate the electric potential on the surface of shell A.

Answer»

`(sigma)/(epsilon_(0))[(a^(2)-B^(2))/(a)+c]`
`(sigma)/(epsilon_(0))[(a^(2)-b^(2))/(b)+c]`
`(sigma)/(epsilon_(0))[(a^(2)-b^(2))/(b)+a]`
`(sigma)/(epsilon_(0))[(a^(2)-b^(2))/(c)+a]`

SOLUTION :
Potential ins.ide the shell and on SURFACE is same
`V = (KQ)/(R)`
where R is radius of shell and potential at `r gt R` distance `V= (kq)/(R)`
`Vb = (kq_(a))/(b) + (kq_(b))/(b) +(kq_(c))/(b)` but ` Q = 4p pi^(2) sigma`
`:. Vb = (4pia^(2)sigma)/(4pi in_(0)xxb)+(4pi b^(2)(-sigma))/(4 pi in_(0)xxb) +(4pi in^(2)(sigma))/(4pi in_(0)xxc)`
`= (a^(2)sigma)/(in_(0)b)-(b^(2)sigma)/(in_(0)b)+(c^(2)sigma)/(in_(0)c)`
`= (sigma)/(in_(0))[(a^(2)-b^(2))/(b)+c]`


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