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JEE Advance - Physics (2008 - Paper 2 Offline - No. 14)

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

The electric field at r = R is :
independent of a
directly proportional to a
directly proportional to a$$^2$$
inversely proportional to a

Explanation

IIT-JEE 2008 Paper 2 Offline Physics - Electrostatics Question 11 English Explanation

At $$r = R$$,

By applying Gauss law,

$$\phi = {{{q_{enclosed}}} \over {{\varepsilon _0}}}$$

$$ \Rightarrow \oint {E.ds = {{{q_{enclosed}}} \over {{\varepsilon _0}}}} $$

$$ \Rightarrow E\oint {ds = {{{q_{enclosed}}} \over {{\varepsilon _0}}}} $$

$$ \Rightarrow E.4\pi {R^2} = {{Ze} \over {{\varepsilon _0}}}$$

$$ \Rightarrow E = {1 \over {4\pi {\varepsilon _0}}}{{Ze} \over {{R^2}}}$$

i.e., $$E\,\mu {1 \over {{R^2}}}$$

Here, electric field is independent of 'a'.

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