Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = \frac{{\rm{A}}}{{{{\rm{r}}^2}}}{{\rm{e}}^{ - 2{\rm{r}}/{\rm{a}}}}\), where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:

\({\rm{a\;log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\)

\({\rm{a}}\;{\rm{log}}\left( {1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}} \right)\)

\(\frac{{\rm{a}}}{2}{\rm{log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\)

\(\frac{{\rm{a}}}{2}{\rm{log}}\left( {1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}} \right)\)

Charge is distributed within a sphere of radius R with a volume charge

1.	Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = \frac{{\rm{A}}}{{{{\rm{r}}^2}}}{{\rm{e}}^{ - 2{\rm{r}}/{\rm{a}}}}\), where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
A.	\({\rm{a}}\;{\rm{log}}\left( {1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}} \right)\)
B.	\(\frac{{\rm{a}}}{2}{\rm{log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\)
C.	\({\rm{a\;log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\)
D.	\(\frac{{\rm{a}}}{2}{\rm{log}}\left( {1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}} \right)\)
Answer» C. \({\rm{a\;log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\)

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Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = \frac{{\rm{A}}}{{{{\rm{r}}^2}}}{{\rm{e}}^{ - 2{\rm{r}}/{\rm{a}}}}\), where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
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Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = \frac{{\rm{A}}}{{{{\rm{r}}^2}}}{{\rm{e}}^{ - 2{\rm{r}}/{\rm{a}}}}\), where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:

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