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JEE Main 202227 JulyMorning Shift
Exam
JEE Main
Year
2022
Date
27 July
Shift
Morning Shift
Subject
Physics
Chapter
Electrostatics

JEE Main 2022 · 27 July · Morning Shift · Physics · Electrostatics

A long cylindrical volume contains a uniformly distributed charge...

A long cylindrical volume contains a uniformly distributed charge of density ρCm−3ρC{m}^{- 3}. The electric field inside the cylindrical volume at a distance x=2ε0ρmx = \dfrac{2{ε}_{0}}{ρ}m from its axis is _____ Vm−1V{m}^{- 1}.

A long cylindrical volume contains a uniformly distributed charge of density ρC m ^ - 3 . The electric field inside the

Correct answer

0

Step-by-step solution

Given here, Volume charge density =ρCm−3= ρC{m}^{- 3}.

Consider a Gaussian cylindrical surface of height hh and radius xx.

Let qq charge is enclosed by the cylinder of radius xx.

A long cylindrical volume contains a uniformly distributed charge of density ρC m ^ - 3 . The electric field inside the

From Gauss's law,

∫EdScos0=qε0∫ E d Scos0 = \dfrac{q}{{ε}_{0}}

Here, q=q =volume charge density×\timesvolume of imaginary cylinder.

⇒E(2\pixh)=ρ×πx2hε0⇒ E\left(2\pixh\right) = \dfrac{ρ \times \pi{x}^{2}h}{{ε}_{0}}

⇒E=ρx2ε0⇒ E = \dfrac{ρx}{2{ε}_{0}}

⇒E=ρ2ε0×2ε0ρ=1⇒ E = \dfrac{ρ}{2{ε}_{0}} \times \dfrac{2{ε}_{0}}{ρ} = 1

Thus, electric field is 1Vm−11V{m}^{- 1}.

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