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/(4πε_o ) 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 dE_h 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