A uniformly charged rod extends from \(y=-150 \mathrm{~mm}\) to \(y=+150 \mathrm{~mm}\) along the \(y\) axis of an \(x y\) coordinate system. The charge on the rod is \(30 \mathrm{nC}\).

(a) With the goal of eventually calculating the electric field magnitude along the rod's perpendicular bisector, approximate the rod as three charged particles, and draw a picture showing the locations of the three particles you will use for the calculation and the magnitude of the charge on each one.

(b) What is the electric field magnitude at \(x=200 \mathrm{~mm}\) using this approximation?

(c) What is the error in your result in part \(b\) ?

(d) If you were unable to integrate, what could you do to your approximation to make it better?