Find the electric field at the centre of a uniformly charged semicircular ring of radius R. Linear charge density is `lamda`

Explanation

`vec(dE) = dE_(x)hat(i) + dE_(y) hat(j)` on solving `E_("net") = (K lambda)/(R ) = (hat(i) + hat(j))`,
Electric field due to ring on its axis :
`E_("net") = (KQx)/([R^(2) + x^(2)]^(3//2))`

E will be max when `(dE)/(dx) = 0`, that is at `x = (R )/(sqrt(2))` and `E_("max") = (2KQ)/(3sqrt(3)R^(2))`
Case (i) : if `x gt gt R, E = (KQ)/(x^(2))` Hence the ring will act like a point charge
Case (ii) : if `x lt lt R, E = (KQ x)/(R^(3))`