Paragraph: The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R . The charge density (r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as

Correct answer: A. independent of a At r=R , from Gauss's law or aligned E(4 ^2) & = q_ net _0 =(Z e)/( _0) E & =(1)/(4 π _0) · (Z e)/(R^2) aligned E is independent of ' a ' correct option is (a).

JEE Advanced 2008Paper 2

Exam: JEE Advanced
Year: 2008
Paper: Paper 2
Subject: Physics
Chapter: Electrostatics

JEE Advanced 2008 · Paper 2 · Physics · Electrostatics

Paragraph: The nuclear charge (Ze) is non-uniformly distributed...

Paragraph: The nuclear charge

(\mathrm{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. Paragraph: The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R . The charge density (r)

Paragraph: The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R . The charge density (r)

Question: The electric field at

r=R

Options

Aindependent of $a$
Bdirectly proportional to $a$
Cdirectly proportional to $a^2$
Dinversely proportional to $a$

Correct answer

A. independent of $a$

Step-by-step solution

r=R

, from Gauss's law or

\begin{aligned}E\left(4 \piR^2\right) & =\frac{q_{\text{net }}}{\varepsilon_0}=\frac{Z e}{\varepsilon_0}\\ E & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e}{R^2} \end{aligned}

is independent of '

'

\therefore$ correct option is (a).

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