# Electric field at any point on the axis of a uniformly charged ring

## This topic discuss about the Electric field at any point on the axis of a uniformly charged ring .

Expression for the electric field intensity at a point on the axis of the charged ring –

Question may be asked as ; A charge is distributed uniformly over a ring  of radius ‘a’ . Obtain an expression for the electric field intensity E at a point on the axis of the ring. Hence show that for points at large distance from the ring behaves like a point charge.

Suppose a uniform circular ring of radius ‘a’ charged uniformly ‘Q’ which is distributed uniformly over the ring.

Suppose a small element ‘dl’ on the ring then, charge on the element is given by – dQ = (Q/2∏a) dl

The electric field at point p due to this element is given by  –

*****At the place of ∑ students can use integration with limit 0 to 2∏a ( in both case answer will be same ) *****

The field E is directed along the axis OP of the charged ring .

If r >> a , then the above expression may be written as ‘

E =  (Q/4∏ϵ0 r2 )  . This shows that for far points at long distance from the ring , it behaves like a point charge .

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