A charge Q is distributed uniformly within the material of a hollow sphere of inner and outer radii `r_(1)` and `r_(2)` the electric field at distance x from centre for `r_(1) lt x lt r_(2)` will be :-

Options

A. `(Q(x^(3)-r_(1)^(3)))/(4pi in_(0)x^(2)r_(2)^(3))`
B. `(Q(x^(3)-r_(1)^(3)))/(4pi in_(0)x^(2)(r_(2)^(3)-r_(1)^(3)))`
C. `(Qx)/(4pi in_(0)(r_(2)^(3)-r_(1)^(3)))`
D. `(Q(x^(3)-r_(1)^(3)))/(4pi in_(0)r_(1)^(2)(r_(2)^(2)-r_(1)^(2)))`

Answer

B

Explanation

`oint vec(E).vec(ds)=(q_("in"))/(in_(0)) , E.4pix^(2)=(Q xx(4)/(3)pi(x^(3)-r_(1)^(3)))/((4)/(3)pi(r_(2)^(3)-r_(1)^(3)))// in_(0)`
`E=(Q)/(4pi in_(0)x^(2))((x^(3)-r_(1)^(3))/(r_(2)^(3)-r_(1)^(3)))`