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Let there be a spherically symmetric charge distribution with charge density varying as `rho(r)=rho(5/4-r/R)` upto `r=R`, and `rho(r)=0` for `rgtR`, where r is the distance from the origin. The electric field at a distance r(rltR) from the origin is given byA. `(rho_(0)r)/(4epsilon_(0)) ((5)/(4)-(r)/(R))`B. `(4pi rho_(0)r)/(3 epsilon_(0)) ((5)/(3)-(r)/(R))`C. `(rho_(0)r)/(4epsilon_(0)) ((5)/(3)-(r)/(R))`D. `(4rho_(0)r)/(3epsilon_(0)) ((5)/(4)-(r)/(R))` |
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Answer» Correct Answer - C `int vec(E). dvec(A) = (Sigmaq)/(epsilon_(0))` `E (4pir^(2)) = (1)/(epsilon_(0)) int rho dV` `Sigma q = int_(0)^(r) rho dV = int_(0)^(r) rho_(0) ((5)/(4)-(r)/(R)) 4pir^(2)dr` `Sigma q = 4pi rho_(0) [(5)/(4)((r^(3))/(3))-(1)/(R)((r^(4))/(4))]` `E (4pir^(2)) = (4pi rho_(0))/(epsilon_(0)) [(5)/(4)((r^(3))/(3))-(r^(4))/(4R)]` |
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