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

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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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