SATHEE: electrostatic-potential-and-capacitance Question 15

Electrostatic Potential And Capacitance

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electrostatic-potential-and-capacitance Question 15

Question: Q. 8. Three concentric metallic shells $A, B$ and $C$ of rádii $a, b$ and $c (a < b < c)$ have surface charge densities $+ σ, - σ$ and $+ σ$ respectively as shown in the figure.

If shells $A$ and $C$ are at the same potential, then obtain the relation between the radii $a, b$ and $c$ .

U] [Foreign Set-III, 2014]

Show Answer

Solution:

Ans. $q_{A} = σ .4 π a^{2}, q_{B} = - σ .4 π b^{2}, q_{c} = σ .4 π c^{2}$ ,

$\begin{aligned} V_{A} & = k [\frac{q_{A}}{a} + \frac{q_{B}}{b} + \frac{q_{C}}{c}] V_{C} & = k [\frac{q_{A} + q_{B} + q_{C}}{c}] ∵, V_{A} & = V_{C}, we have k [\frac{q_{A}}{a} + \frac{q_{B}}{b} + \frac{q_{C}}{c}] & = k [\frac{q_{A} + q_{B} + q_{C}}{c}] ∴ \frac{q_{A}}{a} + \frac{q_{B}}{b} & = \frac{q_{A} + q_{B}}{c} \end{aligned}$

Putting the values of $q_{A}$ and $q_{B}$ ,

We get

$a + b = c$

Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 15

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Electrostatic Potential And Capacitance

electrostatic-potential-and-capacitance Question 15

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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