Saved Bookmarks
| 1. |
Three concentric metallic shells A , B and C of radii a, b and c (a lt b lt c) have surface densities + sigma ,- sigma and +sigma respectively as shown in Fig. Obtain the expressions for the potential of three shells A , B and C . |
|
Answer» Solution :We know that potential at a POINT either on the surface or inside a charged SPHERICAL shell having surface density `sigma` is `V = (sigma R)/(in_(0))` , where R is radius of shell . The potential at a point OUTSIDE the charged shell at a distance (where `r GT R`) is V = `(sigma R^(2))/(in_(0) r)` In present question `sigma_(A) = + sigma , sigma_(B) = - sigma` and `sigma_(c) = + sigma` , moreover `a lt b lt c` `therefore` Electric potential at shell A , `V_(A) = (sigma A * a)/(in_(0)) + (sigma_(B) * b)/(in_(0)) + (sigma_(C) * c)/(in_(0)) = (sigma a)/(in_(0)) - (sigma b)/(in_(0)) + (sigma_(c) )/(in_(0)) = (sigma)/(in_0) [a -b + c]"" ..... (i)` Electric potential at shell B , `V_(B) = (sigma_(A) * a^(2))/(in_(0) b) + (sigma _(B) * b)/(in_(0)) + (sigma_(c) * c)/(in_(0)) = (sigma * a^(2))/(in_(0) b) - (sigma *b)/(in_(0)) + (sigma * c)/(in_(0)) = (sigma)/(in_(0)) [ (a^(2))/(b) - b + c] ""..... (ii) ` and electric potential at shell C . `V_(C)= (sigma_(A) * a^(2))/(in_(0) c) + (sigma_(B) * b^(2))/(in_(0) c) + (sigma_(c) * c)/(in_0)) = (sigma a^(2))/(in_(0) c) - (sigma b^(2))/(in_(0) c) + (sigma_(c))/(in_(0)) = (sigma)/(in_(0)) [ (a^(2) - b^(2))/(c) + c] "" ... (iii)` |
|