Electric field of Continuous charge Distribution

[amninder15]

A line of positive charge is formed into a semicircle of radius R = 57.8 cm, as shown in the figure below. (The figure is a semicircle above the x-axis with angle θ measured from positive y
axis centred at the origin)

The charge per unit length along the semicircle is described by the expression λ(θ) = λ0cosθ. The total charge on the semicircle is 13.2 µC.
(a) Calculate the value of the constant λ0.
(b) Calculate the total force on a charge of 3.11 µC placed at the center of curvature.

I did part a i found the answer 1.14e-05 C/m. but for part (b) i can't seem to setup the integral

any help would be appreciated.

 

[Simon Bridge]

You need to find the force due to a small part of the semi-circle at angle θ which is inside the arc Rdθ, then integrate that over the whole range of θ.

Where do you get stuck?