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By symmetry, the electric field must point radially outward from the wire at each point; that is, the field lines lie in planes perpendicular to the wire. In solving for the magnitude of the radial electric field E(r) produced by a line charge with charge density λ, one should use a cylindrical Gaussian surface whose axis is the line charge. The length of the cylindrical surface L should cancel out of the expression for E(r).
Apply Gauss's law to this situation to find an expression for E(r).

Respuesta :

Answer:

Explanation:

  • The concept of Gauss Law and charge density is applied to solve the problem.
  • Gauss law states that the total electric fields at any point on a closed gaussian surface is equal to the ratio of the net charge enclosed by that surface.
  • Mathematically from Gauss law ; EA = Q /ε.............equation1
  • from Linear charge density λ = Q/L
  • Q = λL = net charge enclosed
  • For cylindrical surface ; A = 2πrL = area

L = Length of charged object

E = electric field

plugging the expressions in equation1

E(r) x 2πrL = λL/ε

E(r) = λL/2πrLε which is the expression for the radial electric field

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