Question

26. Electric field at the centre 'O' of a semicircle of radius
'a' having linear charge density 2 is given as :-​

Answer 1

Answer:

Consider a small element of length dl and charge = dq = λ dl  , at which point the radius makes an angle θ with the vertical through the center of geometry of the semi circle.

K = 1/(4πε)  

dE = K dq/a²    ,   makes an angle θ with the vertical.

The components along the y axis (vertical) add up.   The limits are θ = -π/2 to π/2.

dl = a dθ

dE_y = (K λ /a) Cos θ dθ

integrating,   E = (K λ / a)  [sinθ ]  from θ = -pi/2  to pi/2

E = 2 K λ/a

Explanation: