Solution : Electrostatic field created by a hemisphere surface charge - Corrected electromagnetism exercises

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Electrostatic field created by a hemisphere surface charge.

 

The z axis is the axis of symmetry of load distribution. The field M is carried by this axis.

Consider a semi-sphere surface element centered at a point P.

Elemental electrostatic field created by this element at the point M of the axis Oz is expressed as:

Only the projection of this vector onto axis Oz contributes to the field at point M:

so :

and

Where:

By integration:

Gold:

Either:

Let:

for:

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