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Corrected Exercises Gauss Theorem - Corrected exercises electromagnetism

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∎ 1. Hydrogen Atom ~ ∎ ( The solution ) ∎ 2. Study of a cylindrical charge distribution. ~ ∎ ( The solution ) ∎ 3. Crossing a charged layer ~ ∎ (The solution ) ∎ 4. Field on the axis of a circular opening of a plan. ~ ∎ ( The Solution ) ∎ 5. Field in a spherical cavity. ~ ∎ ( The solution ) ∎ 6. Research Officer of the electrostatic field generated by a half-charged sphere surface. ∎ 7. Study of a spherical inhomogeneous distribution. ~ ∎ ( The Solution ) ∎ 8. field in the vicinity of the axis of a uniformly charged hoop ~ ∎ ( The Solution ) ∎ 9. uniform volumetric density between two planes ► See the list of electromagnetism corrected exercises

Uniform volume density between two planes - Corrected Exercises Gauss Theorem

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Consider two infinite planes x = - a and x = a. The space between the two planes has a volume density of uniform and constant ρ loads. For x> a and x <- a, it reigns on vacuum . Show that at any point of space, the electrostatic field of this distribution can be written . Expressing Ex for the different parts of space and plot the Ex a function of x. Determine for each region the potential V (x) adopting V (0) = 0. Draw the graph of V (x) in terms of x. It is assumed that a approaches 0 and that the multiplication  ρa remains finite. Set an areal density limit load and look for Ex   on a classic result. ► See solution ► See the list of electromagnetism exercises

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

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► Return to the exercise 1. electrostatic field at a point on the axis of the ring. The planes containing the axis Oz are symmetry planes of load distribution  ; at a point M of this axis, the direction of the electrostatic field must belong to each plan so they intersect: with So: where: As the plane containing the hoop is also a load distribution of the symmetry plane was at a point M' is symmetrical of M from the hoop:       with: Finally, we get to any point on the axis of the hoop: 2. Field in a spot close to the axis. We work in cylindrical coordinates. For any point M of space, the plane containing the point M and the axis Oz is a plane of symmetry of the charge distribution. The field is contained in the plan. Furthermore as there invariance of the charge distribution by rotation about axis Oz we can write the electrostat

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

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►See the solution 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. ►See the solution ► See the list of electromagnetism exercises