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# Need clarity, kindly explain! - Charge is distributed within a sphere of radius R with a volume charge density , where A and a are c - Electrostatics - JEE Main

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

• Option 1)

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

• Option 2)

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

• Option 3)

$a\log \left ( 1-\frac{Q}{2\pi Aa} \right )$

• Option 4)

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

Views

Volume Charge distribution -

$\dpi{100} \left ( \rho \right )-$ charge per unit volume.

$\dpi{100} \rho=\frac{Q}{V}=\frac{C}{m^{3}}=Cm^{-3}$

- wherein

(charge on a dielect ric sphere etc)

$Q=\int \rho\: dV$

$=\int_{0}^{R}\frac{A}{r^{2}}e^{-2\frac{r}{a}}(4 \pi r^{2})dr$

$=2 \pi a A(1-e^{-2\frac{R}{a}})$

$R=\frac{a}{2}\log (\frac{1}{1-\frac{Q}{2 \pi a A}})$

Option 1)

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

Option 2)

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

Option 3)

$a\log \left ( 1-\frac{Q}{2\pi Aa} \right )$

Option 4)

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

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