Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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# A Long Cylindrical Wire Carries a Positive Charge of Linear Density 2 ⋅ 0 × 10 − 8 - Physics

ConceptElectric Field Introduction of Electric Field

#### Question

A long cylindrical wire carries a positive charge of linear density  2.0 × 10-8 C      m -1 An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. Note that it is independent of the radius.

#### Solution

Let the linear charge density of the wire be λ.
The electric field due to a charge distributed on a wire at a  perpendicular distance rfrom the wire,

"E"  = λ/ (2 pi ∈ _0 "r")

The electrostatic force on the electron will provide the electron the necessary centripetal force required by it to move in a circular orbit. Thus,

"qE" = ("m""v"^2)/"r"

⇒ mv2 = qEr  .. (1)

Kinetic energy of the electron,"K" = 1/2 mv2

From (1),

"K" = ("qEr")/2

"K" = "qr"/2  λ /(2 pi ∈_0 "r")    [∵ "E" = λ/((2 pi ∈_0 "r")) ]

K =(1.6 ×10-19) × ( 2 × 10-8) × ( 9 × 109)J

K = 2.88 × 10-17 J

Is there an error in this question or solution?

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Solution A Long Cylindrical Wire Carries a Positive Charge of Linear Density 2 ⋅ 0 × 10 − 8 Concept: Electric Field - Introduction of Electric Field.
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