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### Exercise Field Lines - electrostatic potential

Considering the electrostatic fieldin a plane defined by its components in polar coordinates:
Determine the equation of the field lines.

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### Solution : Potential created by a cone portion - electrostatic potential - Corrected exercises electromagnetism

∎ Back to exercise Consider a surface element S on the truncated cone centered about the point P. The Elemental electrostatic potential created at the point O of the axis Ox by a surface element dS centered about the point P is expressed as:
so :
We get :

By integration:
We get :

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### Potential created by a cone portion - electrostatic potential - Corrected exercises electromagnetism

Consider a portion of a cone ,of half-angle with the vertex a and  limit rays R1 and R2 (R1 <R2).
This system is loaded on the surface with non-uniform density:

a is a constant homogeneous to a length and r the radius of the cone at a point on its axis of symmetry.
Determine the electrostatic potential  at the vertex O of the cone.

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### Potential field created by a hemisphere charged on surface - electrostatic potential - Corrected exercises electromagnetism

Considering a half sphere of center O, of radius R, uniformly charged on surface with the surface density σ.
1. Determine the electrostatic potential at a point M of the axis Oz of symmetry of this hemisphere.
2. Deduce the expression of the electrostatic field at that point Mr.
3. Determine the potential and the electrostatic field on O. ( think for limited development).

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