IIT-JEE 2008 · Paper 2 · Physics Q38

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Passage

Paragraph for Question Nos. 36 to 38

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 radial distance $r$ from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

ρ(r) against r: constant at d from r = 0 to r = a, then falling linearly to zero at r = R.

The electric field within the nucleus is generally observed to be linearly dependent on $r$ . This implies

a=0

a=\frac R2

a=R

a=\frac{2R}3

Answer and worked solution

Official answer: C

$E\propto r$ inside means $\frac{q(r)}{r^2}\propto r$ , i.e. $q(r)\propto r^3$ : a uniform charge density throughout. That is the flat part of the graph extending all the way to the surface: $a=R$ .

(C)

Topics:Electric flux and Gauss's law

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IIT-JEE 2008 · Paper 2, Physics question 38