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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)/(3epsilon_(0))(5/4-r/R)`B. `(4pirho_(0)r)/(3epsilon_(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 Total charge `Q=underset(0)overset(tau)(int)rho dV=underset(0)overset(tau)(int)rho_(0)(5/4-r/R)4pi r^(2)dr` `=4pi rho_(0) underset(0)overset(tau)(int)((5r^(2))/4-r^(3)/R)dr=4pi rho_(0)[(5r^(3))/12-r^(4)/(4R)]` `E=(KQ)/r^(2)=1/(4pi in_(0)r^(2))4pi rho_(0)[5/12 r^(3)-r^(4)/(4R)]` `=(rho_(0)r)/(4 in_(0))[5/3-r/R]` |
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