A line of positive charge is formed into a semicircle of radius R = 40.0 cm. The charge per unit length along the semicircle is described by the expression λ = λ0 cos(θ). The total charge on the semicircle is 15.0 µC. The semi circle starts off at 0 and finishes at pi going through quadrants I and II. Calculate the magnitude of the total force on a charge of 2.00 µC placed at the center of curvature. θ is to be taken to start off from pi/2 thus creating a triangle with R that cos(θ)= y/R and sin(θ)=x/R
The Attempt at a Solution
I replaced ldql with λRdθ. then I found lambda to be 1.194x10-5 since I know the length of the semicircle and total charge Q. I plugged this into the integral to find E(electric field) and got Ex=kλ/R∫sin(θ) ⇔ kλ/R (-cosθ). this should give me the magnitude of the electric field. then I multiplied this time the charge of 2.00μC placed at the center of the curvature. Where am I going wrong? Any response would be greatly appreciated.