A rod of length L has a total charge Q distributed uniformly along its length. It is bent in the shape of a semicircle. Find the magnitude of the electric field at the centre of curvature of the semicircle.

Explanation

` dq=Q/LRd theta `
Net electric field have only vertical component
` =intdEcos theta `
` =1/(4piepsilon_0)Q/Lint_(-pi/2)^(pi/2)(Rd theta)/(R^2)cos theta `
` =1/(4piepsilon_0)Q/(LR)[sin theta]_(-pi/2)^(pi/2) `
` 1/(4piepsilon_0)Q/(LR)[1-0(-1)] `
` (2Q)/(4piepsilon_0LR)=Q/(2piepsilonL^2) (:.piR=L)`.