If an insulated non-conducting sphere of radius R has charge density . The electric field at a distance r from the centre of sphere (r R) will be

Correct answer: C. ( r)/(3 _0) Charge which is enclosed in the surface is given by σ=(4)/(3) π r^3 Now according to Gaussian law aligned φ E d s & =σ, _0 E 4 π r^2=(4)/(3) π r^3 E & =( r)/(3 _0) aligned

JIPMER 2005

Exam: JIPMER
Year: 2005
Subject: Physics
Chapter: Electrostatics

JIPMER 2005 · Physics · Electrostatics

If an insulated non-conducting sphere of radius R has charge...

If an insulated non-conducting sphere of radius

R

has charge density

\rho

. The electric field at a distance

r

from the centre of sphere

(r \gt R)

will be

Options

A $\frac{\rho R}{3 \varepsilon_0}$
B $\frac{\rho r}{\varepsilon_0}$
C $\frac{\rho r}{3 \varepsilon_0}$
D $\frac{3 \rho R}{\varepsilon_0}$

Correct answer

C. $\frac{\rho r}{3 \varepsilon_0}$

Step-by-step solution

Charge which is enclosed in the surface is given by

\quad \sigma=\frac{4}{3} \pi r^3 \rho

Now according to Gaussian law

\begin{aligned} \varepsilon \phi E d s & =\sigma, \varepsilon_0 E 4 \pi r^2=\frac{4}{3} \pi r^3 \rho \\ E & =\frac{\rho r}{3 \varepsilon_0}\end{aligned}

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