Electrostatics and Magnetostatics
Charged ring equivalent to a dipole
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Let a thin ring (A), of center O and radius , be divided in two equally evenly charged parts and .
By using the notion of electrostatic dipole, determine the potential and the electrostatic field at a point M, very far away from O ( ).
Try to cut the circle in small elementary dipoles.
Let's cut the circle in small elementary dipoles delimited by the angle .
The elementary dipole moment is :
The symmetry shows that the resulting dipole vector is oriented as .
It is worth :
Let's consider a point M located in the plane (Oyz), and let's write the angle between axis and (OM) line.
The potential created by the ring becomes :
The electric field is expressed by: