SATHEE: electrostatic-potential-and-capacitance Question 16

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 16

Question: Q. 9. N spherical droplets, each of radius $r$ , have been charged to have a potential $V$ each. If all these droplets were to coalesce to form a single large drop, what would be the potential of this large drop ?

(It is given that the capacitance of a sphere of radius $x$ equals $4 π ε_{0} k r$ .)

A] [CBSE SQP 2013]

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Solution:

Ans. Total (initial) charge on all the droplets

$= N \times (4 π ε_{0} k r V)$

Also

$N \times \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3}$

$∴ R = N^{1 / 3} r$

If $V^{'}$ is the potential of the large drop, we have

$\begin{aligned} 4 π ε_{0} k R \times V^{'} & = N \times 4 π ε_{0} k r \times V & 1 / 2 ∴ & V^{'} & = \frac{N r}{R} \cdot V = N^{2 / 3} V & 1 / 2 \end{aligned}$

[AI Q. 10. Find the IBF. associated with a charge $q$ if it were presenf the point $P$ with respect to the ‘setup’ of two charged spheres, arranged as shown. Here $O$ is the mid-point of the line $O_{1} O_{2}$ .

A [CBSE SQP 2013]

Ans.

$\begin{aligned} r_{1} = O_{1} P = \sqrt{r^{2} + (2 a + b)^{2}} 1 / 2 & r_{2} = O_{2} P = \sqrt{r^{2} + (a + 2 b)^{2}} 1 / 2 & ∴ V = \frac{1}{4 π ε_{0}} [\frac{Q_{1}}{r_{1}} + \frac{Q_{2}}{r_{2}}] \end{aligned}$

$∴$ P.E. of charge, $q$ , at $P = q V$

$= \frac{q}{4 π ε_{0}} [\frac{Q_{1}}{{[r^{2} + (2 a + b)^{2}]}^{1 / 2}} + \frac{Q_{2}}{{[r^{2} + (a + 2 b)^{2}]}^{1 / 2}}]$

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 16

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Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 16

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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