Question

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

Answer 1

`lambda=` linear charge density.
The are is the collection of large no. of point charges. Consider a part of ring as an element of length `Rdtheta` which subtends an angle `dtheta` at centre of ring and it lies between `theta` and `theta + d theta`
`vec(dE)=dE_(x) hat(i)+dE_(y) hat(j), E_(x)= int dE_(x)=0` (due to symmetry)
& `E_(y)=int dE_(y)= underset(0)overset(pi)(int) dE sin theta =(K lambda)/R underset(0)overset(pi)(int) sin theta. dtheta=(2Klambda)/R`