JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Electrostatics

The nuclear charge

(Z e)

is non-uniformly distributed within a nucleus of radius

R

. The charge density

ρ (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.

The electric field within the nucleus is generally observed to be linearly dependent on

r

. This implies

(A) $a = 0$
(B) $a = \frac{R}{2}$
(C) $a = R$ ✓ Correct
(D) $a = \frac{2 R}{3}$

Answer: (C)

Solution

For the electric field to be linearly dependent on

r

(i.e.,

E \propto r

), the charge density must be constant within the nucleus.

This is because by Gauss's law:

E (r) \cdot 4 π r^{2} = \frac{Q _{e n c} ( r )}{ε _{0}}

For

E \propto r

, we need

Q_{e n c} \propto r^{3}

, which means

ρ

must be constant.

From the figure,

ρ

is constant when the linear variation starts at

r = a

and remains constant. For

ρ

to be constant throughout,

a = R

(the density is constant from center to surface).

JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Single correct option

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JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Electrostatics

Solution

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