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Electrostatics

Gauss's law

Using Gauss's law, derive an expression for the electric field at a distance r from an infinitely long straight uniformly charged wire (linear charge density λ).

LA
Hard
5 Marks
90% Confidence

Confidence Score

90%

Times Viewed

0

Max Marks

5

Hints

  • 1.cylindrical Gaussian surface
  • 2.use symmetry, E radial and constant
  • 3.charge enclosed = λL

Answer Outline

  1. 1.Choose a cylindrical Gaussian surface of length L
  2. 2.Compute enclosed charge Q_enc = λL
  3. 3.Apply Gauss's law ΦE = EA = Q_enc/ε₀
  4. 4.Solve for E: E = λ/(2πε₀r)

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