### Field Exercise Solution created by a hemisphere surface charge

**1.**

*O*electrostatic field.
The

*z*axis is the axis of symmetry of load distribution. Field*O*is carried by this axis.
Consider a surface element of the half sphere centered

*at*a point P. Elemental electrostatic field created by this element*to*the point O of*the*axis Oz is expressed as:
Only the projection of this vector onto

*axis*Oz contributes to the field at the point*O:**O*is:

**2. Electrostatic Field in M.**

The

*z*axis is the axis of symmetry of load distribution. The field*M*is carried by this axis.
Consider a surface element of the half sphere 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:
Gold :

and

where: By integration:

Gold :

Either:

Let:

For :

The limit is calculated

## Comments

## Post a Comment