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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 )

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A admin

 

Volume Charge distribution -

\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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