IIT-JEE 2008 · Paper 2 · Physics Q36

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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 at $r=R$ is

independent of

a

directly proportional to

a

directly proportional to

a^2

inversely proportional to

a

Answer and worked solution

Official answer: A

Gauss's law at r = R. All the charge $Ze$ is enclosed, whatever its distribution:
$E(R)=\frac{Ze}{4\pi\varepsilon_0R^2},$
independent of $a$ .

(A)

Topics:Electric flux and Gauss's law

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IIT-JEE 2008 · Paper 2, Physics question 36