Charge is distributed within a sphere of radius R with a volume charge density rho(r) = (A/r²)(e)⁻²ʳ/ᵃ , where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
(A) a log [1 - (Q/2πaA)]
(B) a log [ 1/(1 - (Q/2πaA))]
(C) (a/2) log [ 1/(1 - (Q/2πaA))]
(D) (a/2) log [1 - (1/2πaA)]
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Answer:
A. will be correct answers
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Thus the value of radius is R = a/2 log [ 1 / 1 - Q/ 2πaA]
Option (C) is correct.
Explanation:
Q = ∫ pdv
Q = ∫ R - 0 a/r^2 e^-2r/a (4πr^2dx)
Q = 4πA ∫ R - 0 e^-2r/a dx
Q = 4πA (e^-2r/a / -2/a)
Q = 4πA ( - a/2) v - 1)(e^-2r/a - 1)
Q = 2πaA ( 1 - e^-2r/a )
R = a/2 log [ 1 / 1 - Q/ 2πaA]
Thus the value of radius is R = a/2 log [ 1 / 1 - Q/ 2πaA]
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