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 at

r = R

(A)independent of $a$ ✓ Correct
(B)directly proportional to $a$
(C)directly proportional to $a^{2}$
(D)inversely proportional to $a$

Answer: (A)

Solution

By Gauss's law, the electric field at

r = R

(on the surface) depends only on the total charge enclosed, which is

Z e

, regardless of how the charge is distributed inside.

E (R) = \frac{Z e}{4 π ε _{0} R ^{2}}

This is independent of the parameter

a

that describes the charge distribution.

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

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