Solution : Potential field created by a disc at a point on its axis of revolution - electrostatic potential - Corrected exercises electromagnetism

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1. The potential at a point M of the axis.

Consider a surface area element of the disk centered at a point P. The electrostatic potential created at a point M of the axis Oz is expressed as:

Since r and θ variables are separated :

For the calculation is performed following variable change:

For :

On the other hand :

We get :

Taking the zero potential at infinity is obtained:

2. Field at a point M of the axis.

The z axis is axis of symmetry of the charge distribution. The field at a point M of the axis is carried by this axis:

We must therefore calculate the derivative of the function .

We have: x = y where sh

As

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