# 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? - Physics

Numerical

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 the same length surrounds the previous 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"(2pi"d")"L"

Where d = 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

∴ phi = "E"(2pi"dL") = "q"/in_0

Where,

q = Charge on the inner sphere of the outer cylinder

0 = Permittivity of free space

"E"(2pi"dL") = (lambda"L")/(in_0)

"E" = lambda/(2piin_0"d")

Therefore, the electric field in the space between the two cylinders is E = lambda/(2piin_0"d").

Concept: Relation Between Electric Field and Electrostatic Potential
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 2 Electrostatic Potential and Capacitance
Exercise | Q 2.17 | Page 88
NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Exercise | Q 17 | Page 88

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