Charge is distributed within a sphere of radius R with a volume charge density `p(r)=(A)/(r^(2))e^(-2r//a),` where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

Options

A. `a/2 log(1-Q/(2pi aA))`
B. `a/2 log(1/1-Q/(2pi aA))`
C. `a log(1-Q/(2pi aA))`
D. `a log (1/1-Q/(2pi aA))`

Answer

B

Explanation

`Q= int_0^R p 4 pi r^2 dx, int_0^ R A/r^2 e^((-2r)/a) 4 pi ^2 dr=4 pi A int_0k e^(-2r//a) =(4 pi A)/((-2//a)) [e^(-2r//a) ]_0^R, Q=-2pi A a(e^((-2R)/a)-1)`
`Q=-2 pi A a e ^((-2R)/a) +2 pi a A implies e^(-2R//a)= (2 pi a A-Q)/(2 pi a A) implies R=a/2 log (1/(1-Q/(2pi a A))`