Field in the vicinity of the axis of a uniformly charged hoop - Corrected Exercises Gauss Theorem

 

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A hoop of radius R, center O, carries the linear  uniform load λ.

1.         Determining the expression of the electrostatic field created by the hoop at a point M of the axis Oz.

2.         It is proposed to calculate now the field in the vicinity of the axis of the hoop.

Using a Gaussian surface having the form of a small Oz axis of cylinder of radius r and of length dz and by assuming that E _z (r, z) = E _{z (axis)} to a point close to the axis, show that the radial component of the field is related to the value of the field axis by:

Determine

at a point closest to the axis.

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