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Irodov Solutions : Problem 3.10

A point charge q is placed at the centre of a thin circular ring of radius R with uniformly distributed charge -q. Find the magnitude of the electric field strength at the point lying on the axis of the ring at a distance x from its centre, if x>>R.

We have to find the resultant electric field strength vector at a point P which is located at a distance x>>R from the centre of the ring. If E₁ and E₂ be the individual field vectors (at point P) due to the point charge +q and the ring charge - q respectively then by superposition principle of electrostatic fields the resultant field vector at point P would simply be the vector addition of E₁ and E₂

We may further note from this obtained expression that the field strength is inversely proportional to the fourth power of the distance for points x>>R. Hence in that region the resultant field decays much rapidly.