SATHEE: electric-charges-and-fields Question 21

Electric Charges And Fields

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electric-charges-and-fields Question 21

Question: Q. 4. A charge $+ Q$ , is uniformly distributed within a sphere of radius $R$ . Find the electric field, due to this charge distribution, at a distant point $r$ from the centre of the sphere where :

(i) $0 < r < R$

(ii) $r$

A [Foreign, 2016]

Show Answer

Solution:

Ans. We have

$E = \frac{1}{4 π ε_{0}} \frac{q}{r^{2}}, for a point charge$

Now (volume) charge density

$ρ = \frac{Q}{(\frac{4 π}{3} R^{3})}$

(i) $∴$ Charge contained within a sphere of radius $r$ $(0 < r < R)$

$Q^{'} = ρ \cdot \frac{4 π}{3} \cdot r^{3} = Q (\frac{r^{3}}{R^{3}})$

$∴$ Electric Field,

$E = \frac{1}{4 π ε_{0}} \cdot \frac{Q^{'}}{r^{2}} = (\frac{1}{4 π ε_{0}} \cdot \frac{Q}{R^{3}} \cdot r) 1 / 2$

(ii) For $r > R$

Electric field $= ($ Electric field due to a point charge $Q$ at the centre) 1

$E = \frac{1}{4 π ε_{0}} \cdot \frac{Q}{r^{2}}$

[CBSE Marking Scheme, 2016]

Electric Charges And Fields

electric-charges-and-fields Question 21

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Electric Charges And Fields

electric-charges-and-fields Question 21

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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