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A Long Charged Cylinder of Linear Charged Density λ is Surrounded by a Hollow Co-axial Conducting Cylinder. What is the Electric Field in the Space Between the Two Cylinders? - CBSE (Science) Class 12 - Physics

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Question

A long charged cylinder of linear charged density λ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

Solution

Charge density of the long charged cylinder of length L and radius r is λ.

Another cylinder of same length surrounds the pervious cylinder. The radius of this cylinder is R.

Let E be the electric field produced in the space between the two cylinders.

Electric flux through the Gaussian surface is given by Gauss’s theorem as,

`phi=E(2pid)L`

Where, = Distance of a point from the common axis of the cylinders

Let q be the total charge on the cylinder.

It can be written as

`therefore phi=E(2pidL)=q/in_0`

Where,

q = Charge on the inner sphere of the outer cylinder

0 = Permittivity of free space

`E(2pidL)=(lambdaL)/(in_0)`

`E=lambda/(2piin_0d)`

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 2: Electrostatic Potential and Capacitance
Q: 17 | Page no. 88

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Solution A Long Charged Cylinder of Linear Charged Density λ is Surrounded by a Hollow Co-axial Conducting Cylinder. What is the Electric Field in the Space Between the Two Cylinders? Concept: Relation Between Electric Field and Electrostatic Potential.
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