Three nonconducting infinite sheets are parallel to each other. Each sheet has a uniform surface charge density. Sheet 1 is negatively charged with surface charge density \(-\sigma\), and is defined to be the plane \(x=0\). Sheet 2 has an unknown surface charge density and is at a distance of 2.0 \(m\) to the right of sheet 1 . Sheet 3 , negatively charged with surface charge density \(-3 \sigma\), is located further to the right of Sheet 2 at a distance of \(2.0 \mathrm{~m}\) from sheet 2 . The electric field is zero at a point between Sheet 1 and Sheet 2, at a distance of \(0.5 \mathrm{~m}\) from Sheet 1.

(a) What is the surface charge density on sheet 2 ? What is the electric field at

(b) \(x=-1.0 \mathrm{~m}\),

(c) \(x=3.0 \mathrm{~m}\),

(d) \(x=7.0 \mathrm{~m}\) ?