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 Homework Statement:

A uniformly loaded semicircleshaped wire of radius R has a linear density of charge lambda. An electric field magnitude of 10 N / C is measured at the center of the semicircle. We straighten this same wire and we note an electric field magnitude of 8 N / C, this time at a distance of 2 m on its perpendicular bisector; the field thus measured is directed towards the wire.
a) Calculate the values of the lambda and R
b) How many electrons would need to be added or removed from the wire in order for it to become neutral? Specify whether to add or remove electrons
c) Calculate the vector electric force on a proton placed at the center of curvature of the wire
when the latter is in the shape of a semicircle
 Relevant Equations:

At the center of the semicircle an electric field magnitude of 10 N / C
Straighten wire has an electric field magnitude of 8 N / C
Electric field for the semicircle
$$E =  \frac {πKλ} {2R} $$
In this case E is equals to 10 N/C
Electric field for the straighten wire
$$E = 2Kλ * ( 1  \frac {2y} {\sqrt{4y^2 + L^2}})$$
In this case E is equals to 8 N/C
What I'm searching is R, λ, and the length of the wire, so I think I may need a third equation ?
Not sure if I took the right approach for this.
Thank you.
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