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d derive an expression for electric field intensity due to uniformly charged ring on it axix
Asked by kalsichaitanya | 30 Dec, 2023, 04:08: PM

Let us consider a charge ring of radius R . Let q be the total charge uniformly distibuted over its circumference.

Linear charge density  λ = q / (2πR) .........................(1)

Let us consider a small length dl of ring so that its charge content dq = λdl .

Electric field dE at a point P which is at a distance z from center Oof ring  is

where K = 1/(4πεo ) is Coulomb's constant

Axial component of electric field at P is

................................... (2)

Axial component of electric field due to full ring is determined by integrating above expression .

Integration of horizontal component dEh vanishes due to symmetry .

Axial component of electric field due to full ring is

If we substitute , q = λ (2πR) from eqn.(1) , then we get axial electric field as

Answered by Thiyagarajan K | 31 Dec, 2023, 10:25: PM

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