CBSE Class 12-science Answered
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